Question

Simplified Systems has an outstanding issue of $1000-par-value bonds with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date.

1. If bonds of similar risk are currently earning a 10% rate of return, how much should the Simplified Systems bond sell for today?
2. Describe the two possible reasons why similar-risk bonds are currently earning a return below the coupon interest rate on the Simplified Systems bond.

3. If the required return were at 12% instead of 10%, what would be the current value of Simplified Systems’ bond? Contrast this finding with your findings in part a and discuss.

Bonds Valuation Formula

Formulas:

1. Basic bond valuation for annual interest rate

B_o = I * (PVIFA _{rd, n}) + M *  (PVIF _{rd, n})

• Where B_o = value of the bond value = (Vd)
• M = Maturity Value (par value)
• C = coupon interest rate
• I represent an interest paid in dollars (coupon payment in dollars):
• I = coupon interest rate (C ) *  par value (M);
• PVIFA = present value interest factors for one-dollar annuity discounted at r for n periods. Corresponding values are obtained from the financial table.
• rd = the average rate of return investors requires to invest in the bond.         
•   n = number of years (periods)
• PVIF = present value interest factors for one dollar discounted at r for n periods.

2. Bond valuation for interest paid semi-annual

B_o =  * (PVIFA _{rd/2, 2n}) + M * (PVIF _{rd/2, 2n})

Answer 1

If the bonds with similar risk are earning 10% YTM today, the Bond should sell for 1156.47:-

I = coupon interest rate (C ) *  par value (M) = 12% * 1000 = $120

B_o = I * (PVIFA _{10, 16}) + M *  (PVIF _{10, 16})

B_o = 120 * 7.8237 + 1000 * 0.21763

B_o = 938.84 + 217.63 = 1156.47

Two possible reasons why similar-risk bonds are currently earning a return below the coupon interest rate on the Simplified Systems bond are:-

1) Fall in the interest rates in the macro-economy due to which investor return expectation has falled and accordingly, the bonds are trading at a return below th coupon interest rate.

2) The credit rating of the company/bonds have improved post their intial issue, due to which credit risk on the bonds has decreased. and accordingly, the bonds are trading at a return below th coupon interest rate.

If the required return were at 12% instead of 10%, what would be the current value of Simplified Systems’ bond? Contrast this finding with your findings in part a and discuss.

If the required return were at 12%, the bond would be trading at its face value of $1000 and would be giving the coupon interest and the same would be the required return.

This is in contrast to the current price of $1156.47 where the bond is giving a Yield to Maturity of 10% and was therefore trading higher than the face value as the state coupon rate was more than the required return.