Questions

Question 1

  1. Early Saver:

FVA10 = $1,000(FVIFA8%, 10) = $1,000(14.487) = $14,487

FV40 = $14,487(FVIF8%, 40) = $14,487(21.725) = $314,730.08

 

Late Saver: FVA40 = $1,000(FVIFA8% ,40) = $1,000(259.057) = $259,057

 

  1. b) The Early Saver brother’s investment program is better off or worth more as he began saving sooner than later. He is better off by ($314,730.08-$259,057) $55,673.08.

 

Question 2

  1. Value of stock = D1/ (k – g)

= $2.00/(0.14-0.04) = $20

 

  1. Value of stock = D1/ (k – g)

40 = 2.00/ (k – 0.04)

40((k – 0.04) = 2.00

40k – 1.6 = 2.00

k= 0.09

Required rate of return = 9%

 

Question 3

Value of the bond       = PV of annuity + PV of single cash flow

PV of annuity                         = Interest*PVIFA6%, 30 years

= (0.04*1000)*13.765 = $550.60

PV of single cash flow            = Face value*PVIF6%, 30years

=1000*0.17411= $174.11

Value of the bond= $550.60 + $174.11 = $724.71

 

Question 4

Expected return (mean), μ = 15 and standard deviation σ = 25.

  1. less than 20%

For x = 20, the z-value z = (20 – 15) / 25 = 0.2

Hence P(x < 20) = P(z < 0.2) = [area to the left of 0.2] = 0.5793

  1. more than 5%

For x = 5, the z-value z = (5 – 15) / 25 = -0.4

Hence P(x ˃ 5) = P(z ˃ -0.4) = [area to the right of -0.4] = 0.3446

P(x ˃ 5) = 1.00-0.3446 = 0.6554

 

Question 5

  1. Calculation of the relevant cash flow
 
Item Initial 1st Year 2nd Year 3rd Year 4th Year 5th Year
           
Purchase of the new equipment -70000          
           
After-tax production savings (1-0.4)*26000 15600 15600 15600 15600 15600
Depreciation 23331 31115 10367 5187 0
Depreciation tax savings (0.4*depreciation expense) 9332.4 12446 4146.8 2074.8 0
           
Terminal year cash flow          
Salvage value         10000
Tax on Salvage value 0.4(10000-5187)         1925.2
          8074.8
           
Net cash flow -70000 24932.4 28046 19746.8 17674.8 23674.8
BV in year 4 $70000*0.0741 = 5187

 

 

  1. Calculation of NPV and PI
  Year Net Cash flow PV @ 12%
  0 -70000 -70,000
  1 24932.4 22,262.14
  2 28046 22,358.27
  3 19746.8 14,055.77
  4 17674.8 11,232.34
  5 23674.8 13,433.08
  NPV 13,342

 

PI

Profitability Index = (NPV + Initial investment) ÷ Initial Investment

PI = (70000+13342)/70000 = 1.191

 

  1. The project should be accepted because it has a negative NPV ($13,342) and a PI of more than one.
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