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The term structure of spot interest rates is given in the table below
The term structure of spot interest rates is given in the table below. Term Spot interest rate 1.5% 3% 5% For a three-year bond with par value 1000 and annual coupon rate 4%, find: a) The price of the bond. b) Find the annual effective yield rate i for the bond if it is sold at the price in (a). (You may wish to write the equation of value which could earn partial credit if your result is wrong.) 1 year 2 year 3 year
Expert Solution
ANSWER (a)
COMPUTATION OF PRICE OF BOND
| YEAR (IN YEARS) | Spot Rates (IN %) | CASH FLOWS = COUPON = 0.04*$1000= $40 (IN $) | CASH FLOWS = Principal repayment = $1000 (IN $) | Total Cash Flows (IN $) | DISCOUNT FACTOR USING RESPECTIVE SPOT RATES (WORKING NOTE 1) = d(t) | DISCOUNTED CASH FLOWS (IN $) |
| 1 | 1.50 | 40.00 | - | 40.00 | 0.985222 | 39.41 |
| 2 | 3.00 | 40.00 | - | 40.00 | 0.942596 | 37.70 |
| 3 | 5.00 | 40.00 | 1,000.00 | 1,040.00 | 0.863838 | 898.39 |
| PRICE OF BOND | 975.50 |
WORKING NOTE 1
Respective Discount Factors
Year 1:
Spot Rate = 1.5%
d(1) = 1/(1.015) = 0.985222
Year 2:
Spot Rate = 3%
d(2) = 1/(1.03)2 = 0.942596
Year 3:
Spot Rate = 5%
d(3) = 1/(1.05)3 = 0.863838
Answer (b)
Effective Annual Yield Rate using Formula used for computing Approx. YTM
Approx. YTM = [C + (F-P)/n]/[(F+P)/2]
= [40 + (1000-975.50)/3]/[(1000+975.50)/2]
= 0.04875
= 4.875%
Where
C = Coupon = $40
F = Par Value = $1000
P = Price of Bond = $975.50 (Computed in part a)
n = Life of Bond = 3 years
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