VALUATION OF CORPORATE BONDS
A $10,000,4 percent corporation bond paying semiannual dividends is redeemable at 102
at the end of 15 years. What is the maximum price an investor should pay for this bond if
he desires a return of 6 percent compounded semiannually?
Calculation Procedure:
- Determine the semiannual dividend and redemption payment
The dividend = (principal, $)i/2 = $10,000(0.04/2) = $200. Also, the redemption payment
= (redemption price/100)(principal) = (102/100)($ 10,000) = $10,200. - Compute the purchase price
Using an interest rate of 6/2 = 3 percent per semiannual period, compute the present
worth of the dividends and the redemption payment. Equate the present worth to the pur-
chase price of the bond. Or, purchase price = (dividend, $)(USPW) + (redemption pay-
ment, $)(SPPW), for i = 3 percent, n = 30. Hence, purchase price = ($200)(19.60) +
($10,200)(0.4120) = $8122.
RATE OF RETURN ON BOND INVESTMENT
A $10,000, 6 percent, 20-year bond paid dividends semiannually and was redeemed at
par. An investor bought the bond for $11,500 at its date of issue and held it to maturity.
What interest rate did the holder earn?
Calculation Procedure:- Record the payment and receipts associated
with the investment
The payment was $11,500 at the date of issue. The receipt for each semiannual interest
period was (6 percent/2)($ 10,000) = $300 for 40 periods. Also, $10,000 was received at
the end of the 40 periods. The correct interest rate is that which will make the payment
equal the receipts. - Select a trial interest rate and compute the results
Selecting an interest rate of 2.5 percent as a trial, compute the value of the receipts at the
date of issue, using the USPW factor for the dividends and the SPPW factor for the prin-
cipal repayment. Or, ($300)(25.103) + $10,000(0.3724) = $11,255. Since the purchase
price exceeded this value, the true interest rate was less than 2.5 percent. - Select another trial interest rate
Repeat the previous calculation, using a 2 percent rate. Or, $300(27.355) + $10,000
(0.4529) = $12,736. - Interpolate linearly between the trial values
Interest rate, % Purchase price, $
2.5 11,25 5
1 11,50 0
2 12,73 6