Exam 2 - Corporate Finance

This is the second test taken in my Corporate Finance class.  I was given a copy of every test that I put on my web page.  None of them were taken without permission.

1. (15 points) Two stocks and several parameters are listed below. From the perspective of a well-diversified investor, determine if each stock is overvalued, undervalued, or correctly valued; based upon the current return of each stock (which may be too high or too low, depending upon the risk level). The risk free rate is 7% and the required return on the market portfolio is 12%.

	Merck	3M
Current return on stock	12%	15%
Standard deviation (s)	25%	35%
Beta (B)	1.1	1.5

The Beta of a stock is the relevant risk when you add the stock to a well-diversified portfolio. The standard deviation of any single stock is irrelevant in a diversified portfolio.

Merck

r	=	rf + B(rm - rf)
	=	0.07 + 1.1[0.12 - 0.07]
	=	0.07 + 0.055
	=	0.125 or 12.5%

 

Merck stock should be priced on the Security Market Line at 12.5% based on its true risk. It is actually priced to yield 12% currently. The stock is OVERPRICED if it is currently priced to yield 12%. The price will have to FALL so that it will eventually be priced to yield 12.5%, the only correct return based on its true risk.

3M

r	=	rf + B(rm - rf)
	=	0.07 + 1.5[0.12 - 0.07]
	=	0.07 + 0.075
	=	0.145 or 14.5%

 

3M stock should be priced on the Security Market Line at 14.5% based on its true risk. It is actually priced to yield 15% currently. The stock is UNDERPRICED if it is currently priced to yield 15%. The price will have to INCREASE so that it will eventually be priced to yield 14.5%, the only correct return based on its true risk.

2. (15 points) Kosmo Kramer only wants to invest in a portfolio of U.S. stocks and, lacking knowledge of international diversification, he is afraid to invest any of his money outside of the U.S. The U.S. market has an expected return of 12% and a standard deviation of 22%. An index mutual fund that matches the Morgan Stanley Europe, Australia, and Far East Index (EAFE) has an expected return of 14% and a standard deviation of 30%. The U.S. market and the EAFE fund have a correlation coefficient of 0.5. Explain to Kramer why he should consider investing in a portfolio that is 57.5% invested in the U.S. and 42.5% invested in the EAFE Fund. Provide the necessary calculations and also explain the significance of your answer.

First calculate the portfolio expected return

E(Rp)	=	XUSE(RUS) + XEAFE E(REAFE)
	=	(0.575)(0.12) + (0.425)(0.14)
	=	0.1285 or 12.85%

Next calculate the portfolio variance: Remember that the very last term, covariance, is equal to the product of the two standard deviations and the correlation coefficient.  s = standard deviation (I can't seem to get an omega symbol on my HTML editor).

s_p² = X_US²s_US² + X_EAFE²s_EAFE² + 2X_USX_EAFE s_US,EAFE
s_p² = (0.575)²(0.22)² + (0.425)²(0.30)² + 2(0.575)(0.425)(0.22)(0.30)(0.50) = 0.048386
Now take the square root of this variance in order to get the standard deviation.

s_p = 0.21997 or about 22%

This portfolio with 57.5% in the U.S. and 42.5% in the EAFE index thus has a higher expected return than being 100% invested in the U.S., but is has the exact same risk level as being all invested the U.S.

3. (20 points) Shiner Brewery Corp. has $60 million of stock and $40 million of bonds (debt) outstanding; measured at current market value. The risk-free rate of interest is 8% and the required rate of return on the market portfolio is 14%. Shiner has an existing asset (unlevered) Beta of 1.2. Shiner's corporate tax rate is 40%. Assume that Shiner has a Beta of debt always equal to zero. Shiner also has a new project that is estimated to have an asset (unlevered) Beta of 0.80. The new project will be funded with Shiner's existing proportion of equity and debt financing. This new project costs $10 million today and will generate after-tax cash flows of $3 million per year for the next 5 years. Should this new project be accepted (find the NPV)?

A. Calculate Shiner's existing Weighted Average Cost of Capital.

Bequity	=	Bassets[1 + (1 - TC) D/E]
	=	(1.2)[1 + (1 - 0.40)(40/60)]
	=	1.68
		*note the D/E ratio is 2/3

Cost of existing equity

rE	=	rf + B(rm - rf)
	=	0.08 + 1.68[0.14 - 0.08]
	=	0.08 + 0.1008
		0.1808 or 18.08%

r_D = 8%, assume the Beta of the debt is Zero and the debt is riskless

rWACC	=	[D/(D+E)](1-TC)rD + [E/(D+E)]rE
	=	[40/(40+60)](1-0.4)(0.08)
	=	[60/(40+60)](0.1808)
	=	0.12768 or 12.768%
		*note: D/(D+E) = 0.40 and E/(D+E) = 0.60

B. Calculate the NPV for the new project.

Treat project as a separate mini-firm and get the cost of project equity. First use the project's asset Beta to calculate the project's equity Beta:

Bequity	=	Bassets[1 + (1 - TC)(2/3)]
	=	0.8)[1 + (1 - 0.40)(2/3)]
	=	1.12

rE	=	rf + B(rm - rf)
	=	0.08 + 1.12[0.14 - 0.08]
	=	0.08 + 0.0672
		0.1472 or 14.72%

rproject	=	[D/(D+E)](1-TC)rD + [E/(D+E)]rE
	=	[0.40](1-0.4)(0.08) + [0.60](0.1472)
	=	0.10752 or 10.752%

CF₀ = (-10)
CF₁ = 3
CF₂ = 3
CF₃ = 3
CF₄ = 3
CF₅ = 3

The NPV at a 10.752% project cost of capital equals $1.1572 million

4. (10 points) Calculate this stock's geometric average return for the five year period from 1990 through 1994. You are given the following annual returns for a stock:

Year	Return
1990	-10%
1991	+12%
1992	+23%
1993	-5%
1994	+30%

(1 + r₁₉₉₀)(1 + r₁₉₉₁)(1 + r₁₉₉₂)(1 + r₁₉₉₃)(1 + r₁₉₉₄)

(1 - 0.10)(1 + 0.12)(1 + 0.23)(1 - 0.05)(1 + 0.30) = 1.531202, so $1 grew to $1.53 after 5 years.

The geometric mean return = [1.531202]1/5 - 1 = 0.088946 or 8.8946% per year

PV	=	-1
FV	=	1.5312
n	=	5
I/Y	=	solve	=	8.89%

5. (12 points) Calzone Corp. has a new project. The cost of the new machine is $475,000 and the shipping and installation cost is $125,000. The project requires an initial increase (t=0) in net working capital of $50,000 (increased cash and inventory needed) and this $50,000 is assumed to be recovered when the project ends four years from today. The machine fits into a 3 year IRS MACRS depreciation schedule as follows: Year 1 -- 33%; Year 2 -- 45%; Year 3 -- 15%; Year 4 -- 7%. The project will be terminated at the end of the fourth year (four years from today). If the project is accepted it will increase Calzone's revenue and operating costs by $40,000 and $20,000, respectively, for each of the following four years. The machine is expected to have a salvage value of $6000 when the project is terminated in four years. The corporate tax rate is 34%.

Calculate the project cash flows for year 0 (current cash outflow CF₀) and for year 4 (last year for project, CF₄).

First calculate CF₀. For this part we have:

Net Investment = [Machine + installation/shipping] + Initial change in Net Working Capital
Net Investment = [475,000 + 125,000] + 50,000 = $650,000, an outflow of cash
CF₀ = -$650,000

The "installed cost" is $600,000 [machine plus shipping/installation]; this amount will be depreciated over the project's life.

Now calculate CF₄: Note that CF₄ is the final cash flow of this project, so it will include the "terminal" cash flows associated with the disposal and salvage of the project.

CF₄ = [revenue - costs - depreciation][1 - T] + depreciation + change in NWC + salvage value of equipment - [salvage value - ending book value][T]

CF₄ = [40,000 - 20,000 - 42,000][1 - 0.34] + 42,000 + 50,000 + 6000 - [6000 - 0][0.34] = $81,440

Note: The equipment is fully depreciated after 4 years; there is no more remaining book value. Also, the initial increase in NWC of $50,000 is considered to be recovered at the end of the project when it is no longer needed to support the project.

6. (10 points) The Espresso Roast Corporation is considering the purchase of a new coffee bean roaster and grinder. The revenues are expected to be the same for Espresso Roast no matter which machine is acquired. The Quick-Roast machine has a cost of $75,000 and is expected to last 4 years with operating costs of $12,000 per year. The discount rate or cost of capital is a real rate of 8% per year. The machine will have a salvage value of $10,000. Calculate the Equivalent Annual Annuity of the Quick Roast machine.

This looks better on a timeline, but I will just list the cash flows below:

CF₀ = 75,000
CF₁ = 12,000
CF₂ = 12,000
CF₃ = 12,000
CF4 = (12,000 - 10,000) = 2000 since the machine is sold for $10,000 at the end

Note that CF₀, CF₁, CF₂, CF₃, and CF₄ are all negative since each represents a net cost. Now calculate the Present Value of this stream of uneven cash flows (you can just use the NPV function on the calculator).

At a cost of capital of r = 8%, the Present Value = $107,395.22

Now take the PV of $107,385.22 and express is as the annual payments of an N = 4 year ordinary annuity.

Equivalent Annual Annuity

PV	=	-107,385.22
n	=	4
I/Y	=	8%
PMT	=	solve	=	$32,424.85

7. (6 points) The price of Cougar stock rose by 10% today. Two events happened today that caused the stock price to change: (1) the U.S. industrial production was reported to be 0.5% greater than expected and (2) Cougar announced that its newest drug had performed very well in its latest test. Identify whether each of these events either non-systematic risk or systematic risk.

Item (1) is Systematic Risk since Industrial Production is a macroeconomic event that affects all stocks.
Item (2) is Non-systematic Risk, it has nothing to do with any macroeconomic risk.

8. (12 points) For their investment in risky assets, everyone holds the same world market portfolio of stocks (assume that this happens to be the optimal risky portfolio for a CAPM world). The world market portfolio of stocks has an expected return of 12% and a standard deviation of 25% per year. The risk-free asset has a certain return of 7% per year. Everyone holds some portfolio that is a mix of the world market portfolio and the risk-free asset.

A. Frazier holds a certain mix of the world market portfolio and the risk-free asset, and the total portfolio value is $1,000,000. Calculate the expected return and standard deviation of Frazier's portfolio is he invests a weight of 125% in the world market portfolio.

E(Rp)	=	XstocksE(Rstocks) + Xrf E(Rrf)
	=	(1.25)(0.12) + (-0.25)(0.07)
	=	0.15 - 0.0175
	=	0.1325 or 13.25%

sp	=	(Xstocks)sstocks
	=	(1.25)(0.25)
	=	0.3125 or 31.25%

B. Nutella Corporation common stock has a correlation coefficient of 0.50 with the world market portfolio. Nutella's stock has a standard deviation of 40%. Calculate the Beta of Nutella stock.

Covariance(R_mkt,R_nut) = corr(R_mkt,R_nut)s_mkts_nut = (0.50)(0.40)(0.25) = 0.05

Beta of Nutella stock = [covariance(R_mkt,R_nut)]/variance(R_mkt) = (0.05)/(0.25)2 = 0.80