Question

We consider following yield curve

Maturity	1	2	3	4	5	...	10	..	50
Yield (%)	12	11,5	11	10,5	10	...	9,5	...	9

we are planning to participate in an investment which will be made in 3 years from now.This investment will bring you every year 2 million USD over 7 years. What is the maximum price you will be willing to accept.

Please . Thanks

Answer 1

Interest rate of the proposed investment in three years is the spot rate for 7 years after 3 years from now ie., 3 years forward rate for 7 year maturity (f_3,7)

Yield curve depicts the spot rates for various maturities, as of now.

Given, spot rate for 3 years maturity S3= 11% and Spot rate for 10 years S10= 9.5%

Therefore, forwards rate for 7 years after 3 years=

{[(1+S10)^10 / (1+S3)^3]^1/7}-1

(1+9.5%)^10=2.478228

(1+11%)^3=1.367631

(1+9.5%)^10/(1+11%)^3= 2.478228/1.367631= 1.81205867

[(1+9.5%)^10/(1+11%)^3]^1/7=1.812059^(1/7) = 1.088633641

{[(1+9.5%)^10/(1+11%)^3]^(1/7)}-1= 1.088634 – 1 = 0.88633641 Or, 8.86333641%

Using the above rate as interest rate for 7 years, price of the bond is $ 10.11223056 Million calculated as the present value of annuity as follows:

Present Value of Annuity Payments at the end of each period 1 3 Present value of annuity is calculated using the formula PVA= P*{[1-(1+r)^-n]/r]} 4 Where P= Periodical payments, n= Number of payments. 6 r= Rate of interest per period in decimals All amounts in Million $ Given that 8. 9 Periodical payments (P)= 10 Rate of interest (% p.a)=R= 2 No. of years (N)= 8.86333641 No. of payments a year (t)= 11 12 Calculations: Value Formula Cell reference 13 R/(100*t) D10/(100*G10) 14 Interest rate per period in decimals (r)= 0.088633364 15 No. of periods (n)= N*t G9*G10 (1+r)= 16 1+G14 1.088633364 (1+r)^-n= 17 G16^-G15 0.551859493 [1-(1+r)^-n]= 18 1-G17 0.448140507 [1-(1+r)^-n]/r= p*{[1-(1+r)^-n]/r]} D9*G19 G18/G14 5.056115282 19 20 Present value of annuity PV= 10.11223056