- How is the value of a bond determined? What is the value of a 10-year, $1,000 par value bond with a 10% annual coupon if its required rate of return is 10%?
A bond contains a unique pattern of cash flow containing of a stream of constant payment of interest plus the par return at maturity. The payment of annual coupon is the cash flow which is computed as:
Payment = coupon rate x par value = 0.1 x $1000 = $100. With annual coupon bond of 10% for a period of 10 years, the value of bond is found as follows (using financial calculator);
VB = $100/(1+r)’ + $100/(1+r)2 + …+ $100/(1+r)10 + $1000/ (1+r)10
where r is the coupon rate
= $(90.91 + 82.64 + … + 38.55 + 385.454) = $1000
This can also be computed using this formula
VB = $100(PVIF10%, 10) + $1000(PVIF 10%, 10)
The bond period is 10 year, with annual coupon rate of 10%, and $100 annuity per year and a lump of $1000. The sum payment at a period of 10 years is:
VB= $100((1-1/(1+0.1)10)/0.10 + $1000(1/1+0.10)10)
The present value annuity is $614.64 and the present value maturity value is 385.54. The bond value is therefore the sum of the two which is equal to $1000
Value of the bond= PV annuity + PV maturity value = $(614.46 + 385.54) = $1000
- What would be the value of the bond described in part d if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investorsto require a 13% return? Would we now have a discount or a premium bond?
With rate of 13% , after the rate rose by 3% from 10%, the bond value in this case by use of financial calculator will be:
VB(10‑YR) =$100(PVIFA13%,10)+$1,000(PVIF13%,10)
= $100 ((1- 1/(1+0.13)10)/0.13) + $1,000 (1/(1+0.13)10)
=$542.62+$294.59=$837.21.
Based on this result, the change of rate (increase) resulted to a decline in the value of bond. The rate went above the coupon rate resulted to decline of the bond value below the initial bond value. Thus we will have a discount
- What would happen to the bond’s value if inflation fell and rd declined to 7%?Would we now have a premium or a discount bond?
The coupon rate is reduced from 13% to 7%. The nee bond value is computed as follows;
VB(10‑YR) =$100(PVIFA7%,10)+$1,000(PVIF7%,10)
= $100 ((1- 1/(1+0.07)10)/0.07) + $1,000 (1/(1+0.07)10)
=$702.36+$508.35=$1,210.71.
Based on the computation, the bond value rises above the par value with the reduction of the rate below the initial coupon rate. In this case we will have a premium.
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