Question

Face Value	Coupon Rate	Maturity	Years to maturity	Rate of return	Future Value	Payment	Present Value
$48,000,000	4.5%	1997	5	10%	$1,000	$45	$791.51
$32,000,000	8.25%	2007	15	10%	$1,000	$82.50	$866.89
$100,000,000	12.625%	2017	25	10%	$1,000	$126.25	$$1238.27

Assume that you plan to keep your money invested, and to reinvest all interest receipts, for five years. Assume further that you bought the 5-year bond for $800, and interest rates suddenly fell to 5 percent and remained at that level for five years. Set up a worksheet that could be used to calculate the actual realized rate of return on the bond, but do not (necessarily) complete the calculations. Note that each interest receipt must be compounded to the terminal date and summed, along with the maturity value. Then, the rate of return that equates this terminal value to the initial value of the bond is the bond’s realized return. Assume that the answer is 9.16 percent. How does that value compare with your expected rate of return? What would have happed if interest rates had risen to 15 percent rather than fallen to 5 percent? How would the results have differed if you had bought the 25-year bond rather than the 5-year bond? Do these results suggest that you would be better off or worse off if you buy long-term bonds and then rates change? Explain.  

Answer 1

Solution: Reinvestment of Coupons for 5 years;

Present Value = $800, Interest Rate = 5% pa

Years	0	1	2	3	4	5
Value	$800
Interest Amount @ 5%pa		$40	$40	$40	$40	$40
Reinvestment @ 5%pa		40*(1.04)^4	40*(1.04)^3	40*(1.04)^2	40*(1.04)^1	$40
Reinvestment Amount Realized in 5th year		$         48.62	$       46.31	$       44.10	$       42.00	$ 40.00

Total Return at the time of Maturity= 48.62+46.31+44.10+42+840= $1021

CAGR (Compounded Annual Growth Rate) = (1021/800)^(1/5) -1 = 5%

Here, Assumed rate of return is 9.16% but Realized Rate of Return is 5%, which is quiet low as compare to assumed one but equal to lowered rate.

If Rate increased to 15% then Realized Rate of Return or CAGR will be 6%.

As per the data given above for three bonds, it is evident that long term investment in bonds give more return than short term bond investment.