Question

A bond of Visador corporation pays $90 in annual interest, with a $1000 par value. The bonds mature in 18 years. The market's required yield to maturity on a comparable-risk bond is 7.5 percent.

A. Calculate the value of the bond.

B. How does the value change if the market's required yield to maturity on a comparable0risk bond (i) increases to 13 percent or (ii) decreases to 4 percent?

C. Interpret your findings in parts a and b.

Answer 1

Given Information: Coupon payment =90, Face value = 1000, YTM = 7.5%, Maturity = 18 years

A. Price of the bond

Price of the bond is the present value of the coupon payment investor is going to receive till maturity alonf with the maturity value discounted at YTM

Price of bond = Coupon payment x cumulative discounting factor @7.5% for 18 years + maturity value x discounting factor @7

5% for 18th year

[ For factors refer you tables of cumulative discount factor and single discount factor or you can calculate on calculator as Cumulative is sum of (100/107.5) + (100/107.5)² + ........+ (100/107.5)¹⁸ ] and 18th year (100/107.5)¹⁸ ]

= 90 x 9.706009009 + 1000 x 0.272049313

Value of bond = 1145.59 approx

B. How does the value change at i) YTM 13% ii) YTM 4%

i) at YTM 13%

Value of the Bond as per the same formula as above and instead of factor @7.5% use 13% factors.

= 90 x 6.839905233 + 1000 x 0.110812308

= 615.5915 + 110.81231

= 726.40

ii) YTM 4%

Value of the Bond as per the same formula as above and instead of factor @7.5% use 4% factors.

= 90 x 12.65929682 + 1000 x 0.493628109

= 1139.3367 + 493.628109

= 1632.96

iii) Interpretation:

Value of bond at 7.5% is 1145.59 When YTM increased to 13% value of bond reduced to 726.40 and when YTM drops to 4% the price of bond surge to 1632.96. This shows there is inverse realtion between the YTM and price of the bond. When one increase the other go down and vice versa.

There are two reasons behind this, one is logical and other is mathematical.

As per Mathematics, when you discount with the higher rate the factors are lower result in lower Present value and when you use lower rate the cash flows discount at higher factors so price is more than high rate.

Logical reason is, when YTM increases to 13% it means there are other securities available in the market that provide 13% return so investor dumps that bond and rush to other security, they will continue to dump that bond it reach the price where there is indifference between the returns of both the bond. Same with when YTM decreases to 4% investors jump to 7.5% bond continue to buy this till it reach the price where both reach at indifference point. Market participants will not let the abnormal gain sustain for longer period because everyone is keen to grab this.