Question

Consider a firm that currently has a market value of $2,000,000. The firm is considering a project with the following yearly cash flows and a required return (hurdle rate) of 12%. T=0 -1,500,000 T=1 400,000 T=2 -200,000 T=3 900,000 T=4 700,000 T=5 500,000 a) What is the NPV of the project? b) Calculate the Modified IRR (MIRR) using a 12% discount rate. c) If the firm decided to go forward with (i.e., accept) this project, what would the firm's new market value be? Explain your answer clearly and make sure to support your conclusion with the appropriate work.

MACRS Depreciation Percentages -- Half-Year Convention

PROPERTY CLASS

RECOVERY

_________________________________________

YEAR 3-YEAR 5-YEAR 7-YEAR 10-YEAR

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1 33.33% 20.00% 14.29% 10.00%

2 44.45 32.00 24.49 18.00

3 14.81 19.20 17.49 14.40

4 7.41 11.52 12.49 11.52

5 11.52 8.93 9.22

6 5.76 8.92 7.37

7 8.93 6.55

8 4.46 6.55

9 6.56

10 6.55

11 3.28

____________________________________________________

Totals 100.00% 100.00% 100.00% 100.00%

Answer 1

Hurdle rate = 12%
T0 = -1,500,000
This is the Initial Investment for the project.
Cash Flows from the project are
T1 = 400,000
T2 = -200,000
T3 = 900,000
T4 = 700,000
T5 = 500,000

a)
NPV = PV of all Cash Flows - Initial Investment
= 400,000 x PVIF (12%,1) + -200,000 x PVIF (12%,2) + 900,000 x PVIF (12%,3) + 700,000 x PVIF (12%,4) + 500,000 x PVIF (12%,5) - 1,500,000
= 400,000 x .8929 + -200,000 x .7972 + 900,000 x .7118 + 700,000 x .6355 + 500,000 x .5674 - 1,500,000
= 357,160 - 159,440 + 640,620 + 444,850 + 283,700 - 1,500,000
= 1,566,890 - 1,500,000
= 66,890 (Answer)

b)
MIRR = ( FV of positive cash flows / PV of cash outflows )^(1/n) - 1
FV of positive cash flows = 400,000 x 1.12^4 + 900,000 x 1.12^2 + 700,000 x 1.12 + 500,000
= 629407.74 + 1128960 + 784000 + 500,000
= 3,042,367.74
PV of cash outflows = 1,500,000 + 200,000 x PVIF (12%,2)
= 1,500,000 + 200,000 x .7972
= 1,500,000 + 159,440
= 1,659,440

MIRR = (3042367.74 / 1,659,440)^(1/5) - 1
= 1.83^(1/5) - 1
= 1.13 - 1
= .13 i.e. 13%

c)
The Present Market value of the firm = $2,000,000
The new project if added will create a value that is equal to the NPV of the project = $66,890
Hence , the New Market value of the firm = $2,000,000 + $66,890 = $2,066,890