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Finance 340: Fernie Mining Corp's WACC, Payback Period, Tech Selection - Sample Solutions, Exams of Financial Management

Wichita State University (WSU)Financial Management

Solutions to sample problems from a university final exam in financial management i, focusing on fernie mining corporation's weighted average cost of capital (wacc), payback period, and technology selection. Calculations for wacc using three methods, payback period for two technologies, and net present value (npv) and internal rate of return (irr) for each technology.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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Finance 340 – Financial Management I
Summer 2002
Final Exam Sample Problem Solutions
Dr. Stanley D. Longhofer
T-Th 1:30-4:30
1) Fernie Mining Corporation 7% semiannual coupon bonds are currently trading at
$1,050; they have 12 years remaining until maturity. Fernie preferred stock has a par
value of $100 with a 8.25% promised dividend, paid quarterly; the preferred stock is
currently trading at $110 per share. Fernie common stock currently sells for $45 per
share. Its latest dividend was $5.19 per share; dividends are expected to grow by 4%
per year for the foreseeable future.
The risk-free rate is currently 4.5% and average return on the market as a whole is
12.5%. Fernie’s beta is 1.31.
When using the bond-yield-plus-risk-premium approach, Fernie assumes that its
common equity requires a 9.1% risk premium over its own bonds.
Fernie’s corporate marginal tax rate is 40%, and its capital structure includes 50%
common equity, 35% debt, and 15% preferred stock.
Fernie is considering two different technologies for a new mine it will be opening
next year. These technologies are mutually exclusive, so one of the two can be
implemented.
Technology A will require an initial investment of $2.5 million, and will generate
annual net revenues of $750,000 for each the first 3 years and $300,000 for each of
the following 7 years.
Technology B is more expensive to implement, but will allow the mine to be more
productive longer. This technology will require an initial investment of $3.3 million,
and will generate revenues of $625,000 for each of the next 10 years.
a) What is Fernie’s weighted average cost of capital (WACC)? Hint: In calculating
the cost of Fernie’s equity, take the average of the values calculated based on the
discounted cash flow, CAPM, and bond-yield-plus-risk-premium approaches.
The component cost of debt is P/Y = 2, N = 24, PV = − 1,050, PMT = 35,
FV = 1,000 ⇒ I = 6.40%.
The cost of preferred stock is 8.25 / 110 = 7.50%.
The cost of common equity must be calculated using each method.
− DCF: %1604.0
45
)04.1(19.5
0
1=+=+= g
P
D
ks.
− CAPM: %15)045.0125.0(31.1045.0)( =−+=−+= rfmsrfskkkk β.
− BYPRP: ks = 6.40 + 9.10 = 15.5%.
pf3

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Finance 340 – Financial Management I

Summer 2002 Final Exam Sample Problem Solutions

Dr. Stanley D. Longhofer T-Th 1:30-4:

  1. Fernie Mining Corporation 7% semiannual coupon bonds are currently trading at $1,050; they have 12 years remaining until maturity. Fernie preferred stock has a par value of $100 with a 8.25% promised dividend, paid quarterly; the preferred stock is currently trading at $110 per share. Fernie common stock currently sells for $45 per share. Its latest dividend was $5.19 per share; dividends are expected to grow by 4% per year for the foreseeable future. The risk- free rate is currently 4.5% and average return on the market as a whole is 12.5%. Fernie’s beta is 1.31. When using the bond- yield-plus-risk-premium approach, Fernie assumes that its common equity requires a 9.1% risk premium over its own bonds. Fernie’s corporate marginal tax rate is 40%, and its capital structure includes 50% common equity, 35% debt, and 15% preferred stock. Fernie is considering two different technologies for a new mine it will be opening next year. These technologies are mutually exclusive, so one of the two can be implemented. Technology A will require an initial investment of $2.5 million, and will generate annual net revenues of $750,000 for each the first 3 years and $300,000 for each of the following 7 years. Technology B is more expensive to implement, but will allow the mine to be more productive longer. This technology will require an initial investment of $3.3 million, and will generate revenues of $625,000 for each of the next 10 years. a) What is Fernie’s weighted average cost of capital (WACC)? Hint: In calculating the cost of Fernie’s equity, take the average of the values calculated based on the discounted cash flow, CAPM, and bond-yield-plus-risk-premium approaches. The component cost of debt is P/Y = 2, N = 24, PV = − 1,050, PMT = 35, FV = 1,000 ⇒ I = 6.40%. The cost of preferred stock is 8.25 / 110 = 7.50%. The cost of common equity must be calculated using each method.

− DCF: 0. 04 16 % 45

0

= 1 + g = + = P

D

ks.

− CAPM: k (^) s = krf + β (^) s ( km − krf )= 0. 045 + 1. 31 ( 0. 125 − 0. 045 )= 15 %.

− BYPRP: ks = 6.40 + 9.10 = 15.5%.

Thus, the cost of common equity is ks = (16 + 15 + 15.5) / 3 = 15.5%. The firm’s WACC is therefore WACC = 0.35 × 6.40 (1 − 0.40) + 0.15 × 7.

  • 0.50 × 15.5 = 10.22%.

b) Calculate the payback period for each technology. If Fernie requires any project to pay back its initial investment within 4 years, which technology will it accept? Technology A − $750,000 × 3 = $2.250 million. Thus, in the 4th^ year there are still $250,000 in up- front costs to recover. 250 / 300 = 0.83, so payback occurs in 3.83 years for Technology A. Technology B − Since this technology provides constant annual cash flows, payback occurs in 3,300,000 / 625,000 = 5.28 years. Based on the payback method, only Technology A is acceptable.

c) Calculate the discounted payback period for Technology A only given the WACC calculated in part a. Year Cash Flow DCF Cum. DCF 0 ($2,500,000) ($2,500,000) ($2,500,000) 1 750,000 680,457 (1,819,543) 2 750,000 617,363 (1,202,180) 3 750,000 560,119 (642,061) 4 300,000 203,273 (438,788) 5 300,000 184,425 (254,363) 6 300,000 167,324 (87,039) 7 300,000 151,809 64, 8 300,000 137,733 202, 9 300,000 124,962 327, 10 300,000 113,375 440, Thus, payback occurs during the 6th^ year. Since 87,039 / 151,809 = 0.57, the discounted payback period for Technology A is 6.57 years. With a payback requirement of 4 years, this project is no longer acceptable on a discounted payback basis.

d) Calculate the net present value (NPV) of each technology. Based on this method, which of these two technologies should Fernie choose? Technology A − Although we completed the table above for the total cumulative discounted cash flows, we can calculate the NPV using the irregular cash flow worksheet as well. CF0 = − 2,500,000, C01 = 750,000, F01 = 3, C02 = 300,000, F02 = 7, I = 10.22 ⇒ NPV = $440,840. Technology B − Because this technology has constant cash flows, you need not use the irregular cash flow worksheet. Simply use the TVM keys to calculate the present value of the cash flows and subtract off the required initial investment: P/Y = 1, N = 10, I = 10.22, PMT = 625,000, FV = 0 ⇒ PV = − 3,804,326. Thus, NPV = 3,804,326 − 3,300,000 = $504,326.