Question

(Yield to​ maturity) The Saleemi​ Corporation's ​$1,000 bonds pay 5 percent interest annually and have 13 years until maturity. You can purchase the bond for ​$1,075. a.What is the yield to maturity on this​ bond? b.Should you purchase the bond if the yield to maturity on a​ comparable-risk bond is 6 ​percent? a.The yield to maturity on the Saleemi bonds is

Answer 1

Par Value of bond = $1000

Coupon Rate = 5%, so coupon = $50

Maturity = 13 years

Current price = $1075

Current price = 50(P/A,YTM,13) + 1000(P/F,YTM,13)

1075=50(P/A,YTM,13) + 1000(P/F,YTM,13)

BY USING EXCEL

a. YTM = 4.24%

b. Since YTM is less than that same risk bond having YTM of 6%, we should not purchase

Answer 2

a. The yield to maturity of Saleemi bonds is approximately

4.25%

b. The bond should not be purchased

a. The formula for the price of a bond with annual coupon payments is \(P = C\times\frac{1-(1 + r)^{-n}}{r}+\frac{F}{(1 + r)^{n}}\), where P is the bond price, C is the annual coupon payment, F is the face value of the bond, r is the yield to maturity (YTM), and n is the number of remaining periods.

Given that \(F = \$1000\), the coupon rate is \(5\%\), so \(C=1000\times5\%=\$50\), \(n = 13\) years, and \(P=\$1075\).

We can use the trial-and-error method to solve for r. If \(r = 4\%\): The present value of the coupon payments \(PV_{C}=C\times\frac{1-(1 + r)^{-n}}{r}=50\times\frac{1-(1 + 0.04)^{-13}}{0.04}\approx\$499.28\)The present value of the face value \(PV_{F}=\frac{F}{(1 + r)^{n}}=\frac{1000}{(1 + 0.04)^{13}}\approx\$600.57\)The bond value \(V = PV_{C}+PV_{F}=499.28 + 600.57=\$1099.85\)

If \(r = 5\%\): The present value of the coupon payments \(PV_{C}=C\times\frac{1-(1 + r)^{-n}}{r}=50\times\frac{1-(1 + 0.05)^{-13}}{0.05}\approx\$469.68\)The present value of the face value \(PV_{F}=\frac{F}{(1 + r)^{n}}=\frac{1000}{(1 + 0.05)^{13}}\approx\$530.32\)The bond value \(V = PV_{C}+PV_{F}=469.68 + 530.32=\$1000\)

Using linear interpolation: Let \(r_1 = 4\%\), \(V_1 = 1099.85\); \(r_2 = 5\%\), \(V_2 = 1000\); \(V = 1075\)\(r=r_1+\frac{V_1 - V}{V_1 - V_2}(r_2 - r_1)=4\%+\frac{1099.85 - 1075}{1099.85 - 1000}\times(5\% - 4\%)\approx4.25\%\)

So the yield to maturity of the Saleemi bond is approximately \(4.25\%\).

b. Given that the yield to maturity of bonds with the same risk is \(r = 6\%\)When \(r = 6\%\): The present value of the coupon payments \(PV_{C}=C\times\frac{1-(1 + r)^{-n}}{r}=50\times\frac{1-(1 + 0.06)^{-13}}{0.06}\approx\$442.63\)The present value of the face value \(PV_{F}=\frac{F}{(1 + r)^{n}}=\frac{1000}{(1 + 0.06)^{13}}\approx\$468.84\)The bond value \(P = PV_{C}+PV_{F}=442.63 + 468.84=\$911.47\)

Since the market price of the bond is \(P_0 = \$1075\) and \(911.47\lt1075\), that is, the intrinsic value of the bond is lower than the market price. So you should not buy this bond.