Lesson-2

Chapter 3: Analysis of Financial Statements

Chapter 4: Time Value of Money
Discussions Questions (DQs) 
1. Do Problem 3-13 on pp. 113-114.

2. Do Thomson ONE Problem on p. 117.

3. Do Problems 4-1 thru 4-12 on pp. 165-166.

Problem Set 1

3-13: Data for Morton Chip Company and its industry average

(a) Indicated ratios for Morton:

Ratio                                                                              Morton                Industry Analysis

Current Assets/Current Liabilities                                 1.98 times                  2.0          

Days Sale Outstanding                                                   76.29 days                 35.0 days      

Sales/Inventory                                                               6.66 times                 6.7      

Sales/Fixed Assets                                                          5.50 times                 12.1   

Sales/Total Assets                                                           1.70 times                 3.0     

Net Income/Sales                                                            1.7 %                        1.2%

Net Income/Total Assets                                                 2.9%                         3.6%

Net Income/ Common Equity                                         7.6%                          9.0%   

Total Debt/ Total Assets                                                 61.9%                       60.0%

               

Working Note: The Calculation of above ratios is shown below:

·         Current Assets/Current Liabilities = $655,000 / $330,000 = 1.98 times

·         Days Sale Outstanding = Receivables/ (Average Sales per Day) = (Receivables/Annual Sales) 365 days= ($336,000 / $1,607,500) 365 days  = 76.29 days

·         Sales/Inventory =  $1,607,500 / 241,500 = 6.66 times

·         Sales/Fixed Assets =  $1,607,500 / $ 2,92,500 = 5.50 times

·         Sales/Total Assets = $1,607,500 / $ 947,500  = 1.70 times

·         Net Income/Sales = $27,300 / $16,07,500 = 0.017 or 1.7%

·         Net Income/Total Assets = $27,300 / $947,500 = 0.029 or 2.9%

·         Net Income/ Common Equity =  $27,300 / $361,000 = 0.076 or 7.6%                                                                                    

·         Total Debt/ Total Assets = ($330,000 + $256,500) / $947,500 = 0.619 or 61.9%    

(b)    Calculation of Extended Du Pont equation for both Morton and the industry

For Morton:

Return on Common Equity (ROE)

= Return on Assets x Equity multiplier

= (Profit margin x Total assets turnover) x (Equity multiplier)

= (Net Income / Sales) x (Sales / Total Assets) x (Total Assets / Common Equity)

= 1.7% x 1.70 x ($947,500/$361,000)

= 7.6%

          For Industry:

          Return on Common Equity (ROE)

= Return on Assets x Equity multiplier

= (Profit margin x Total assets turnover) x (Equity multiplier)

= (Net Income / Sales) x (Sales / Total Assets) x (Total Assets / Common Equity)

= 1.2% x 3 x (Net Income / Common Equity) ÷ (Net Income / Total Assets)

=1.2% x 3 x (9% ÷ 3.6%)

= 9%

(c)     Strength and Weakness of Morton:

By comparing the Morton ratios with the industry average ratios, we can find the following strengths and weaknesses:

·          Morton’s current ratio (1.98) is lesser than the industry average (2) which shows that it is a good and Morton can pay its short-term obligations at time.

·         Morton’s Days Sales Outstanding (76.29 days) is higher than that of Industry average(35 days) so it is very poor indicating the weakness of Morton's collection of account receivables.

·         Morton’s Inventory turnover ratio is 6.66 which is equivalent to industry average (6.7). It shows that quite satisfactory for Morton.

·         Morton’s fixed asset ratios is 5.50 times which is very lower than industry average(12.1 times) so it indicates that Morton is not using its fixed asset properly.

·         Total assets turnover ratio of Morton (1.7 times) is lesser than average industry (3 times) so it is very poor as compared to industry which shows ineffective utilization of the inventory and assets.

·         Profit margin ratio of Morton (1.7%) is higher than industry average (1.2%) so that it shows Morton’s prices are relatively high and costs are relatively low.

·          Morton’s return on assets is 2.9% which is below the industry average (3.6%) so it shows that low earning power of Morton.

·         Morton’s return on equity (7.6%) is below the industry average (9%) which shows the weakness of Morton.  

·         Morton’s Debt ratio is 61.9% which is higher than average industry (60%) so that it is comparatively satisfactory but not good, and borrowing additional fund should be controlled.

(d)    If Morton had doubled its sales as well as its inventories, account receivables, and common equity during 2010 then it would have certainly affected the validity of ratio analysis. As a result of that, it is likely to increase the Days sales outstanding, total asset ratio, fixed asset ratio and decrease the return on equity, profit margin on sales, and finally there wouldn’t be changed in inventory turnover ratio. Apart from these ratios, no effect can be observed. Thus, financial decisions based on these ratios are likely to be affected by these changes.

References

C. Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi: New Age International Publishers.

Eugene F. Brigham, Michael C. Ehrhardt. (2011). Financial Management: Theory and Practice . Natorp Boulevard Mason, USA: South-Western Cengage Learning.

4- 1. Solution:

Here given,

Present Value (PV)                  = $10,000             

Interest rate (i)                         = 10% 

No. of years (n)                       = 5 years

Future Value (FV)                  = ?

We know that,           

                        FV = PV x (1+i) n

                              = 10,000 x (1+0.1)5     

      = $16,105.10 

Therefore, the amount will be $16,105.10 after five years.

4- 2. Solution:

Here given,

Future Value (FV)                    = $5,000

Interest rate (i)                          = 7%                    

 No. of years (n)                       = 20 years

Present Value (PV)                  =?

We know that,

                         PV = FV x [1/ (1+i)] n 

                   = $5,000 x (1/1.07)20

       = $1292.095

Thus, the present value of a security is $1,292.1

4- 3. Solution:

Here given,

No of years (n)             = 18 years   

Present Value (PV)     = $250,000           

Future Value (FV)      = $1 million          

Interest rate (i)            =?

Here,

FV = PV x (1+i) n    

          $ 1,000,000 = $ 250,000 x (1+i) 18

            (1+i) 18= 4

           1+i= (4)1/18

               i = 1.0801 -1

               i= 0.0801

    i = 8.01%

Thus, the annual interest rate should be of 8.01% p.a. to earn to reach goal with no additional funds.

4- 4. Solution:

Let,

Present Value (PV)     = y

Future value (FV)       = 2y

Interest (i)                   = 6.5% (Given)

No of years (n)            = ?

As we know,

FV       = PV x (1+i) n    

           2y/y      = (1+6.5%) n

           2 = (1.065) n

Taking log on both sides,

  Log (2) = log (1.065) n

  Log (2) = n log (1.065)
           n = log (2)/log (1.065)

                       n = 11.0067

Therefore, it will take approximately 11 years to double the amount deposited at the interest of 6.5%.

4- 5. Solution:

Here given,

Present Value (PV)      = $42,108.53    

Payment (PMT)            = $5,000

Interest rate (i)              = 12%          

Future value (FV)        = $250,000           

No. of years (n)           =?

Here,       

FV= PMT/i x [(1+i) n -1)] + PV x (1 + i) n

  $250,000 = $5000/0.12 x [(1+0.12) n-1] + $42,180.53(1+0.12) n

                    (1.12) n = 3.4786

                    (1.12) n = 3.4786

Taking log on both sides,

                n log 1.12 = log 3.4786

                                         n = 11.0041years

Thus, it will take approx.11 years to reach the goal of $250,000.

4- 6. Solution:

Here given,

Interest rate (i)                        = 7%            

No. of years (n)                       = 5 years     

Payment (PMT)                       = $300 each year          

Future Value (FVA) of an annuity   =?

Here,

     FVA n        = PMT/i x [(1+I) n – 1]

           FVA5 = $300/0.07 x [(1.07)5- 1]

                              = $1725.2217

Therefore, the future value will be $1725.22.

If this were annuity due, the future valued would be,

FVA due=PMT/I [(1+i)n-1] x (1+i)

              = $300/0.07[(1+0.07)5-1] x (1+0.07)

             = $ 1845.9872

4- 7. Solution:

Here given,

Interest Rate (i)           = 8%

Time period (n)           = 6 years  

Where,

Present Value Interest Factor (PVIF) =    1/ (1+r) t   

Present Value = Cash Flow x PVIF     

End of year (t)	Cash Flow	PVIF at 8%	Present Value = Cash flow X PVIF
1	$100	0.9259	$92.59
2	$100	0.8573	$85.73
3	$100	0.7938	$79.38
4	$200	0.7350	$147.00
5	$300	0.6805	$204.15
6	$500	0.6301	$315.05
		Total Present Value	=$ 923.90

Now,

FV       = PV (1+i) n

= $923.90(1+0.08)6

= $1466.1131 

4- 8.  Solution:

Given,

Present Value (PV)         = $20,000,

Time (n)            (12 x 5) = 60 months,

Interest per month           = 12/12 = 1%,

Future Value (FV)          = 0

Payment (PMT)               = ?

EFF                     = ?

We know that,

PMT     = PV (1+r) n [r / [(1+r) n-1}]

                         = $20,000 (1+0.01) 60 x 0.01 / [(1+0.01) 60-1]

 = $444.9

And,

Compounding period (m)                   = 12 months

Monthly interest rate                           = 1%

Here,

            EFF     = (1+Periodic Rate) Compounding period -1

   EEF = (1+i/m) m-1

= (1+0.01)12-1

=12.68%

4-9 (a) Solution:

Given,

Present Value (PV)      = $500        

Time (n)                       =1 year    

Interest rate (i)             = 6%  

Future Value (FV)        =?

Here,

FV = PV (1 + i) n

      = $500(1+0.06)¹

        = $530

Using calculator:

PV = -$500       n=1      i/Y=6        CPT and FV = $530

Thus, the deposit will be $530 at the end of a year.

4-9 (b) Solution:

Given,

Present Value (PV)           = $500  

Time (n)                            =2 year  

Interest rate (i)                  = 6%        

Future Value (FV)            =?

Here,

                        FV       = PV (1 +i) n

            = $500(1+.06)2

            =$561.80

Using calculator:

 PV = -$500 n=2   i/Y=6   CPT and FV = $561.8

Thus, the deposit will be $561.8 at the end of 2 years.

4-9 (c) Solution:

Given,

Future Value (FV)                  = $500  

Time (n)                                   =1 year

Interest rate (i)                        = 6%            

Present Value (PV)                 = ?

Here,

PV       = FV/ (1+i) n

PV       = $500/ (1+0.06)1

= $471.7

Using calculator:

FV = $500    n=1      i/Y = 6      CPT and PV = -$471.6981

Therefore, $471.7 is needed as of today to receive $500 after 1 year at 6% discount rate.

4-9 (d) Solution:

Given,

Future Value (FV)                  = $500  

Time (n)                                   =2 year         

Interest rate (i)                        = 6% 

Present Value (PV)                 =?

Here,

                        PV       = FV/ (1+i) n

PV       = $500/ (1+0.06)2

= $445.0

Using calculator:

FV = $500    n=1      i/Y = 6     CPT and PV = -$444.9982

Therefore, a deposit of $444.9982 is needed as of today to receive $500 after 2 years at 6% discount rate.

4-10 (a) Solution:

Given,

Present (PV)                            = $500    

Time (n)                                   =10 years     

Interest (i)                               = 6%

Future Value (FV)                  =?

Here,

FV       = PV (1 +i) n

FV       = $500(1+.06)10

= $895.4238

Using calculator:

PV = -$500   n=10    i/Y=6    CPT and FV = $895.4238

Thus, the deposit will be $895.4238 at the end of 10 year

4-10 (b) Solution:

Given,

Present Value (PV)                 = $500   

Time (n)                                   =10 years     

Interest rate (i)                        = 12%

Future Value (FV)                  = ?

Here,

FV       = PV (1 +i)n

FV       = $500(1+.12)10

= $1552.92

Using calculator:

PV = -$500     n=10    i/Y=12    CPT and FV = $1552.9241

Thus, the deposit will be $1552.92 at the end of 10 year

4-10 (c) Solution:

Given,

Future Value (FV)                  = $500    

Time (n)                                   =10 year       

Interest rate (i)                        = 6%            

Present Value (PV)                 = ?

Here,

                        PV       = FV/(1+i)n

PV       =$500/(1+0.06) 10

= $279.20

Using calculator:

FV = $500    n=10    i/Y = 6      CPT and PV = -$279.1974

Thus, deposit of $279.20 is needed as of today to receive $500 after 10 years at 6% discount rate.

4-10 (d) Solution:

Given,

Future Value (FV)                  = $500  

Time (n)                                   =10 year       

Interest rate (i)                        = 12%            

Present Value (PV)                 = ?

Here,

PV       = FV/(1+i)n

PV       = $500/(1+0.12)10

= $160.99

Using calculator:

FV = $500    n=10    I/Y = 12     CPT and PV = -$160.9866 

Thus, the deposit of $160.99 is needed as of today to receive $500 after 10 years at 12% discount rate.

4-11 Solution:

Given,

Present Value (PV)     = $200

Future Value (FV)      = 2 x 200

= $400

Time (n)                      = ?

Here,

FV       =PV (1+i) n

       (1+i) n      = FV/PV

4-11 (a) Solution:

            Here, Interest rate (i) = 7%

       (1+i) n      = FV/PV        

        1.07ⁿ        = 400 / 200

        1.07ⁿ        = 2

Taking log both sides,

                       log1.07ⁿ= log2

                       n = log2 / log1.07

                       n = 10.25

                       n = 10 years

Thus, it will take 10 years for $200 to double if it deposited at 7% interest rate. 

4-11 (b) Solution:

           Here, interest rate (i) = 10%

n= log2/log1.1

            n = 7.27 years

Thus, it will take 7.27 years for $200 to double if it deposited at 10% interest rate.

4-11 (c). Solution:

          Here, interest rate (i)  = 18%

n= log2/log1.18

            n = 4.18 years

Thus, it will take 4.18 years for $200 to double if it deposited at 18% interest rate.

4-11 (d). Solution:

             i = 100%

 n = log2/ log2

             n = 1 year

Thus, it will take 1 year for $200 to double if it deposited at 100% interest rate.

4- 12(a) Solution:

Given,

Payment (PMT)           = $400

Time (n)                       = 10 years

Interest rate (i)            = 10%

Future Value (FV)      = ?

Here,

FV    = PMT x [(1+i) n – 1] / i

Using Calculator:

PMT = -$400      PV = 0       n = 10     I/Y = 10     CPT and Press FV

FV = $6374.9698

4- 12(b) Solution:

Given,

Payment (PMT)           = $200

Time (n)                       = 5 years

Interest rate (i)            = 5%

Future Value (FV)      = ?

FV = PMT x [(1+i) n – 1] / i

Using calculator:

PMT = -$200      PV = 0      n = 5       i/Y = 5     CPT and Press FV

FV = $1105.1263

4-12 (c) Solution:

Given,

Payment (PMT)           = $400

Time (n)                       = 5 years

Interest rate (i)            = 0%

Future Value (FV)      = ?

   FV = PMT x [(1+i) n – 1] / i

Using calculator:

PMT = -$400    PV = 0       n = 5         i/Y = 0       CPT and Press FV

   FV = $2000

4-12 (d) solution:

Re-calculating on part a, b and c by assuming as an annuity due is as follows:

First of all changing the setting of the calculator for calculating annuities due

2^nd PMT > 2^nd Enter > 2^nd CPT (Settings Changed for Annuity)

a)          PMT = -$400, PV = 0, n = 10, I/Y = 10, CPT and Press FV

              FV = $7012.4668

b)         PMT = -$200, PV = 0, n = 5, I/Y = 5, CPT and Press FV

              FV = $1160.3826

c)          PMT = -$400,     PV = 0,  n = 5,  I/Y = 0, CPT and Press FV

              FV = $2000

References

C. Paramasivan, T. Subramanian. (2015). Financial Management. New Delhi: New Age International Publishers.

Eugene F. Brigham, Michael C. Ehrhardt. (2011). Financial Management: Theory and Practice . Natorp Boulevard Mason, USA: South-Western Cengage Learning.