Bond price

[thtang]

You have decided to invest in Bond X, an n years bond with semi-annual coupons and the following characteristics
Par value is 1000
The ratio of the semi-annual coupon rate to the desired semi-annual yield rate is 1.03
PV of the redemption value is 381.5
v^n = 0.5889
Calculate the price of bond X

I use the equation
P = K + r/i * (F-K)
P = 381.5 + 1..03 * (1000 - 381.5)
= 1019

but the answer is 1055.

can anybody advice?

Thanks

[ctperng]

You have decided to invest in Bond X, an n years bond with semi-annual coupons and the following characteristics
Par value is 1000
The ratio of the semi-annual coupon rate to the desired semi-annual yield rate is 1.03
PV of the redemption value is 381.5
v^n = 0.5889
Calculate the price of bond X

I use the equation
P = K + r/i * (F-K)
P = 381.5 + 1..03 * (1000 - 381.5)
= 1019

but the answer is 1055.

can anybody advice?

Thanks

In your solution, you didn't use the condition v^n = 0.5889, which is one of the tricky parts.

Also, before you can use P = K + r/i * (F-K), you have to make sure that Face value equals redemption value, i.e. F = C, since the Makeham formula states that

P = K + (g/i)(C-K), which reduces to your formula if C = F. (This is because by definition Fr = Cg, so r = g if F = C.)

It is not very clear what v means, but most likely this is the discounting factor (1+i)^(-1), where i = semi-annual yield. (*)

Under the assumption (*), the redemption value C equals

C = 381.5/v^(2n) = 1100.05, which is not F = 1000. (Therefore you cannot use the formula P = K + r/i * (F-K), as remarked above.)

Once you get C, you can solve g from Fr = Cg to get
g = (F/C)r, then plug in to the Makeham formula to get

P = K + (g/i)(C-K) = K + (F/C)(r/i)(C-K)
= 381.5 + (1000/1100.05)*1.03*(1100.05 - 381.5) = 1054.29, which is close to the answer 1055.

Alternatively (and more directly), you can just apply the "Frank" formula:

P = Fr*a_n + K = Fr*(1-v^(2n)/i + K = F*(r/i)*(1-v^(2n)) + K
= 1000*1.03*(1-.5889^2) + 381.5 = 1054.29.

Hope this helps.

ctperng