Applied Corporate Finance - Final Questions

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Solutions to Practice Problems
by Kyung Hwan Shim University of New South Wales Australian School of Business School of Banking & Finance for FINS 3625 S1 2010 May 23, 2010



These notes are preliminary and under development. They are made available for FINS 3625 S1 2010 students only and may not be distributed or used without the author’s written consent.



1

Solution for Question 1

Summary Table of Cash Flows t=0 I II CF from Machinery ignoring depreciation Working Capital Level in Working Capital CFs from Working Capital III Revenues Variable Costs Fixed Costs Pre Tax Profit Taxes at 34% After Tax Operating CF’s ignoring Deprec. -245,000 160,000 160,000 -160,000 0 0 0 0 0 0 t=1 0 180,000 20,000 -20,000 800,000 450,000 100,000 250,000 85,000 165,000 t=2 0 212,000 32,000 -32,000 900,000 506,250 100,000 293,750 99,875 193,875 t=3 55,000 0 -212,000 +212,000 1,060,000 596,250 100,000 363,750 123,675 240,075

PV of CFs from Tax Shield Gains =

C × d × TC 1 S × d × TC − × n r+d (1 + r) r+d 1 55, 000 × 25% × 34% 245, 000 × .25 × .24 − × = 9% + 25% (1 + .09)3 9% + 25%

= 50, 632.50 20, 000 32, 000 212, 000 − + = −41, 579.50 1.09 1.092 1.093 165, 000 193, 875 240, 075 + + = 499, 939 PV of CFs from Oper. Excl. Dep. = 1.09 1.092 1.093 55, 000 PV of CFs from Invest. & Salvage = −245, 000 + = −202, 530 1.093 1 PV of CFs from Terminal Loss = TC (C(1 − d)n − S) × (1 + r)n 1 = .34(245, 000(1 − .25)3 − 55, 000) × = 12, 696.4 (1 + .09)3 PV of CFs from NWC = −160, 000 −

N P V = 50, 632.50 − 41, 579.50 + 499, 939 − 202, 530 + 12, 696.4 = 319, 158 Since NPV is positive, the firm should go ahead and produce the ultimate tennis racket. Solutions for Question 2

2

(a) The market value of debt is D = .15(1.25M ) × a13 7.4% + = 187, 000 × = 2, 026, 284 The market value of preferred equity is P = 5, 700 shares × $87.75 = $500, 175 The market value of common equity is E= $2.2M × $62.50 = 40, 000 shares × $62.50 = $2, 500, 000 $55 1.25M 1.07413

1 − (1.074)13 + 494, 145 0.074

The cost of debt, preferred equity and common equity are RD = YTM on the debt = 7.4% RP = $7.90 = 0.09 = 9% $87.75

RE = 0.045 + 1.182 × (0.10 − 0.045) = 0.11 = 11% (b) The total value of the firm is V =D+P +E = $2, 026, 284 + $500, 175 + $2, 500, 000 = $5, 026, 459 and its overall cost of capital is D P E × (1 − TC ) × RD + × RP + × RE V V V 500, 175 2, 500, 000 2, 026, 284 = × (1 − .44) × .074 + × .09 + × .11 5, 026, 459 5, 026, 459 5, 026, 459

W ACC =

= 8.04%

(c) $150, 000 × (1 − .44) $84, 000 = = $1, 050, 000 0.08 0.08

3

So, the most that True North can pay for the project and still earn the required rate of return of 8% is $1,050,000. Solutions for Question 3 Drilling Rights = sunk costs NPV = −(Initial Investment) + PV(Tax Shield on drilling costs) + PV(Additional after-tax operating revenues) + PV(Depreciation tax shield on equipment) − (A.T. restoration costs) + PV (Salvage Value) − PV(Lost tax shield on salvage value) + PV(CF due to Terminal Loss or Recapture Depreciation) 15, 000 × 0.4 = − 15, 000 − 5, 000 + 1.15 5, 000(.5)(.4) 1 − (1.015)10 + + 5, 000(1 − .4) × 0.15 5 + .15 1, 000(1 − .4) 1, 000 1 1, 000(.5)(.4) − + − 1.1510 1.1510 1.1510 .5 + .15 1 + .4(5, 000(1 − .5)10 − 1, 000) × (1 + .15)10 = 1, 736.58

Solutions for Questions 4 (a) Initial Investment: Land Net of Capital Gain Tax: − 2(1 + 50%) + (2 × 50%)(40%) = −2.6M Building: − 1M Machinery: − 4 + 1 = −3M PV of Tax Shield Gained: 4M × 20% × 40% = 1.23M 6% + 20%

Initial Investment: 2.6 − 1 − 3 + 1.23 = −$5.37M

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(b) At the end of year 3: Land Net of Capital Gain Tax: 5 − (5 − 2)(40%) = 4.4M Machinery / Building: 2.2M PV of Tax Shield Loss: − 2.2 × 20% × 40% = −0.6769M 6% + 20%

CFs from Recap. Deprec.: 40%(4(1 − 20%)3 − 2.2) = −.0608M Cashflows at the end of year 3 = 4.4 + 2.2 − .6769 − .0608 = 5.8623M (c)

I. Cashflows derived from change in working capital: Year 0 Investment in WC Change in working capital Cf’s from WC investment II....
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