Question

Answer the following questions about a 10-year $1,000 bond with a 3 percent simple interest coupon paid annually at the end of each year, assuming the risk appropriate discount rate is 1.5 percent:

• What amount of interest or cash flow, measured in dollars, would the bondholder receive annually?
• At what point in time will the bondholder be paid the $1,000?
• Calculate the net present value of the bond at its issuance?
• If you could buy the bond at issuance for $1,100 would you? Why or why not?
• What would happen to the net present value of the bond at issuance if riskiness of the bond increased 200 basis points (i.e., the discount rate increased to 3.5%)
• If you could still buy the bond at issuance for $1,100 would you? Why or why not?

Answer 1

What amount of interest or cash flow, measured in dollars, would the bondholder receive annually

Bond Holder Receive Annual Coupon Payment Cn

Cn = Coupon Payment = Coupon Rate * Face Value  

Coupon Rate = 3%

Face Value = 1000

Cn = 3% * 1000 = 30
Ans : amount of interest or cash flow, measured in dollars bondholder receive annually = $ 30 (Ans)

At what point in time will the bondholder be paid the $1,000?

Bond Holder paid the Face Value of the Bond at its maturity. Here maturity is 10 Years.

Ans : Bond holders will receive $1,000? at 10 years i.e on bonds maturity. (Ans)

net present value of the bond at its issuance :  

Present Value of Future Cash Flow of the Bond :

Here,

P = Current Price of the Bond = Face Value * ( 1 - Discount Rate) = 1000 * ( 1 - 1.5%) = 985

Cn = Coupon Payment = Coupon Rate * Face Value = 3% * 1000 = 30

n = 10 Years

r = discount Rate = 1.5% = 0.015

FV = Face Value = 1000

NPV

= -985 + 276.66 + 861.66

= 153.33

Ans : NPV of the issuance = 153.33 (Ans)

If you could buy the bond at issuance for $1,100 would you? Why or why not?

Now if the Bond issuance price increase from 985 to 1100 .

Price Increase = 1100 - 985 = 115

Current NPV = NPV - Price Increase =  153.33 - 115 = 38.33

As still Current NPV > 0 one should Purchase the Bond (Ans)

What would happen to the net present value of the bond at issuance if riskiness of the bond increased 200 basis points (i.e., the discount rate increased to 3.5%)

Current Discount Rate becomes r = 3.5%

P = Current Price of the Bond = Face Value * ( 1 - Discount Rate) = 1000 * ( 1 - 1.5%) = 985

Cn = Coupon Payment = Coupon Rate * Face Value = 3% * 1000 = 30

n = 10 Years

r = discount Rate = 3.5% = 0.035

FV = Face Value = 1000

NPV

= - 985 + 249.49 + 708.91

= -26.5

Ans : NPV of the issuance = - 26.5 (Ans)

If you could still buy the bond at issuance for $1,100 would you? Why or why not?

As calculated NPV of the Bond is already negative. So further increase of issuance will decline NPV more negative.

So no one would prefer to to Purchase the Bond. (Ans)