True, false or “It depends”? Explain briefly in each case.
a. If the nominal interest rate is 8% and expected inflation is 2%, then the
real interest rate is 8 – 2 = 6%
b. A one-year forward price, say for Brent crude oil, reveals investors’
consensus expectation of the Brent spot price that will prevail one year
c. The PV of a cash-flow stream that grows only with inflation (constant
in real terms) can be calculated by dividing the next cash flow by the
difference between the nominal opportunity cost of capital and the
future inflation rate.
d. If the term structure of spot interest rates is upward-sloping, then a
Treasury bond paying a 6% coupon will trade at lower yield to maturity
than a Treasury bond with the same maturity but a 2% coupon.
e. Put-call parity assures that the price of a put and a call are exactly equal,
provided of course that the underlying asset and maturity are the same.
f. If two investments are perfectly negatively correlated ( ρ = − 1),
then the two investments can be combined in a portfolio with zero
g. It makes sense to invest in stocks that have delivered positive
alphas, and to avoid stocks that have generated zero or negative
According to modern portfolio theory, the best portfolio of risky securities is the
portfolio with the highest Sharpe ratio. Explain why this is so. Hint: You will
probably want to draw a plot of portfolio risk and return.
Kansas City Southern railroad (KSU) pays a dividend of DIV = $1.12 per share.
Security analysts forecast 2015 earnings per share at EPS = $5.50. The stock closed
at $114.25 on December 8, 2014.
a. Is the earnings-price ratio EPS/ PKSU = 5.50/114.25 = .048 a plausible
estimate of the true “cost of equity” (rE!) for KSU? Why or why not?
b. Sometimes the following “dividend growth” formula is used to estimate
rE! = DIV
P + g
Security analysts forecast KSU’s EPS growth at 9.95 % per year over the
next five years. Solve for rE using the EPS growth forecast for g. In what
circumstances would your answer be a plausible estimate of the true cost
of equity? Explain.
The current market values of Bariloche Corp’s defined- benefit pension assets
(PA) and liabilities (PL) are:
PA = $1.115 billion
PL = $1.465 billion
Thus the plan is underfunded by $350 million.
The pension assets are invested in a “balanced” portfolio of about 80%
equities and 20% fixed income, with expected return of 8.0% and annual standard
deviation of 14%. The duration of the fixed-income assets is 10 years, and the
duration of PL is 20 years. The term structure is flat at 6%.
a. Bariloche’s CFO is worried about another recession like 2008-2009. She
asks you what would happen if the stock market drops by 20% and the Fed
pushes interest rates down to 4%. (Assume the term structure remains flat.)
Explain how to calculate the approximate changes in PA, PL and the
amount of underfunding. (You can do the calculations if you wish, but a
detailed and specific outline is OK.) Why are these changes
b. A large insurance company offers to take over all the PLs for a one-time
payment of $1.565 billion. The takeover would release the PAs, so the net
cost to Bariloche would be $1.565 − 1.115 = $.450 billion or $450 million.
Several board members argue strongly for this action in order to reduce the
risks that Bariloche’s pension strategy imposes on the company and its
stockholders. Do you agree? Explain.
a. Calculate the after-tax WACC for Federated Junkyards, using the following
• Debt: $750 million book value outstanding. The debt is trading at 95%
of book value. Yield to maturity is 9%.
• Equity: 25 million shares trading at $43 per share. Book value per share
is $30. The expected rate of return on Federated’s stock is 15%.
• Tax rate = .38.
b. A year later, Federated has moved to a more conservative debt policy. Debt is
paid down to $500 million. The yield to maturity has fallen to 8.6% and the
debt is now trading at par value. Shares are now trading at $48 (book value =
$32). Recalculate WACC, assuming that Federated’s business risk,
opportunity cost of capital and tax rate have not changed.
Reliable Electric is considering a proposal to manufacture a new type of industrial
electric motor that would replace most of its existing product line. A research
breakthrough has given Reliable a two-year lead on its competitors. The project
proposal is summarized in Table 6.7 below.
2014 2015 2016–2023
1. Capital expenditure -10,400
2. Research and development -2,000
3.Working capital -4,000
4.Revenue 8,000 16,000 40,000
5. Operating costs -4,000 -8,000 -20,000
6. Overhead -800 -1,600 -4,000
7. Depreciation -1,040 -1,040 -1,040
8. Interest -2,160 -2,160 -2,160
9. Income -2,000 0 3,200 12,800
10. Tax 0 0 420 4,480
11. Net cash flow -16,400 0 2,780 8,320
12. Net present value = +13,932
Table 6.7 Cash flows and present value of Reliable Electric’s proposed investment ($
1. Capital expenditure: $8 million for new machinery and $2.4 million for a warehouse
extension has been charged to this project, although only about half of the warehouse
space is currently needed. Since the new machinery will be housed in an existing factory
building, no charge has been made for land and building.
2. Research and development: $1.82 million spent in 2012. This figure was corrected for
10% inflation from the time of expenditure to date. Thus 1.82×1.1 = $2 million.
3. Working capital: Initial investment in inventories.
4. Revenue: These figures assume sales of 2,000 motors in 2014, 4000 in 2015, and 10,000
per year from 2016 through 2023. The initial unit price of $4,000 is forecasted to remain
constant in real terms.
5. Operating costs: These include all direct and indirect costs. Indirect costs (heat, light,
power, fringe benefits, etc.) are assumed to be 200% of direct labor costs. Operating
costs per unit are forecasted to remain constant in real terms at $2,000.
6. Overhead: Marketing and administrative costs, assumed equal to 10% of revenue.
7. Depreciation: Straight-line for 10 years.
8. Interest: Charged on capital expenditure and working capital at Reliable’s current
borrowing rate of 15%.
9. Income: Revenue less the sum of research and development, operating costs, overhead,
depreciation, and interest.
10. Tax: 35% of income. However, income is negative in 2013. This loss is carried forward
and deducted from taxable income in 2015.
11. Net cash flow for 2014-2023: Assumed equal to income less tax.
12. Net present value: NPV of net cash flow at a 15% discount rate.
Read the notes to the table carefully. Which entries make sense? Which do not? Why
or why not? What additional information would you need to construct a version of
Table 6.7 that makes sense?
Mom and Pop Groceries has a two-year contract to supply groceries to the
government of the Central Antarctic Republic. The contract calls for two payments
of $500,000 after each of two annual shipments arrives by snow train. The first
payment should be received 12 months from now and the second 24 months from
Unfortunately there is a 20% per year chance of a coup d’état, in which case the new
government will not pay. Thus the probability of receiving the first payment is only
80%. If the existing government survives and makes the first payment, Mom and
Pop will face the same 20% risk of non-payment in year two.
Mom and Pop’s controller therefore decides to discount the payment at 32%, rather
than at the company’s 12% cost of capital. (12% + 20% = 32%)
a. What’s wrong with using a 32% discount rate to offset this political risk?
b. How much are the $500,000 payments really worth if the odds of a coup
d’état are 20% in year 1 and again 20% in year 2 if the government
survives in year 1?
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a. False. This is because the nominal interest rate is found using the formula (1 + 8%)/(1 + 2%) – 1. The method showed is an approximation method.
b. True. This is because the investors take long and short positions according to their expectations and that influences the forward rate.
c. False. This is because the next cash flow would be in nominal terms and it cannot be discounted using real discount rate. The real cash flows should be discounted using ...