Principles of Corporate Finance_ 12th Edition

Chapter 26 Managing Risk 701

bre44380_ch26_673-706.indd 701 09/30/15 12:09 PM

22. Duration hedging Securities A, B, and C have the following cash flows:

Period 1 Period 2 Period 3

A $ 40 $40 $ 40

B 120 — —

C 10 10 110

a. Calculate their durations if the interest rate is 8%.

b. Suppose that you have an investment of $10 million in A. What combination of B and C
would hedge this investment against interest rate changes?

c. Now suppose that you have a $10 million investment in B. How would you hedge?

23. Hedge ratios What is meant by “delta” (δ) in the context of hedging? Give examples of how
    delta can be estimated or calculated.


24. Risk management A gold-mining firm is concerned about short-term volatility in its rev-
    enues. Gold currently sells for $1,300 an ounce, but the price is extremely volatile and could
    fall as low as $1,220 or rise as high as $1,380 in the next month. The company will bring
    1,000 ounces to the market next month.

a. What will be total revenues if the firm remains unhedged for gold prices of $1,220, $1,300,
and $1,380 an ounce?

b. The futures price of gold for delivery one month ahead is $1,310. What will be the firm’s
total revenues at each gold price if the firm enters into a one-month futures contract to
deliver 1,000 ounces of gold?

c. What will total revenues be if the firm buys a one-month put option to sell gold for $1,300
an ounce? The put option costs $110 per ounce.

Commodity Spot Price Futures Price Comments

Magnoosium $2,550 per ton $2,728.50 per ton Monthly storage cost = monthly

convenience yield.

Frozen quiche $0.50 per pound $0.514 per pound Six months’ storage costs = $.10

per pound; six months’ convenience

yield = $.05 per pound.

Nevada Hydro 8s of 2002 77 78.39 4% semiannual coupon payment

is due just before futures contract

expires.

Costaguanan pulgas

(currency)

9,300 pulgas = $1 6,900 pulgas = $1 Costaguanan interest rate is 95%

per year.

Establishment Industries

common stock

$95 $97.54 Establishment pays dividends of $2

per quarter. Next dividend is paid

two months from now.

Cheap white wine $12,500 per

10,000-gal. tank

$14,200 per

10,000-gal. tank

Six months’ convenience

yield = $250 per tank. Your

company has surplus storage and

can store 50,000 gallons at no cost.

❱ TABLE 26.4^ Spot and six-month futures prices for selected commodities and securities.
See Problem 19.