Assume that you wish to purchase a 18-year bond that has a maturity value of $1,000...

Assume that you wish to purchase a 18-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $35. If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Solutions

Expert Solution

The maximum amount which we are willing to pay for this bond is actually the present value of the cashflows to be recieved in future or The present value of the bond:

Semi-annual coupon payment = $35

Time periods until maturity(n) =18*2 = 36

Amount until maturity(A) = $1000

YTM (since coupon is semiannual) =10% /2 = 5%

Now, lets calculate the present value using the following formula:

Coupon Payment * PVAF(YTM, n) + Annual Payment * PVF (YTM, n)

35 * PVAF(5%, 36) + 1000 * PVF(5%, 36)

35 *16.54685 + 1000 * 0.1726574

579.1398 + 172.657

751.79

The Price of the bond is $751.79

Maximum Price we should be willing to pay is $751.79

Note 1: PVAF means Present value annuity factor & can be checked from the table or calculated by the following formula:

Note 2: PVF means Present value factor & can be checked from the table orcalculated as follows:

jeff jeffy answered 1 year ago

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