Question

Nick is considering investing in a two year $10,000 bond paying a coupon rate of 4%. The market interest rate is 5%. Calculate the present value (PV) of the bond.

Answer 1

Answer:

$9,813.76        

Explanation:

The net present value of the bond can be calculated using the following formula:

PV of Bond ($) = PV of future coupon payments (Step1) + PV of redemption Amount

So here

PV of Bond ($) =  $743.76 (Step1) + $10,000 x Discount Factor at 5% and 2 years time

PV of Bond ($) = $743.76 + $10,000 / (1+5%)^2 = $743.76 + $9,070

PV of Bond ($) = $9,813.76

Step 1: PV of future coupon payments

And Present value of this annual cash flow that would be received in first 2 years is:

Present Value = Future Annual Cash Inflow (Step2)   * Annuity factor at 5% and at 2 years time

Present Value = $400 * [1  -  (1+r)^-n] / r

= $400 * [1  - (1+5%)^-2] / 5%  = $400 x 1.8594 = $743.76

Step 2: Future Annual Cash Inflow

Annual return is the coupon interest received, so this implies that:

Annual Cash Inflow = Face value * Coupon rate

Here

Face value of the bond is $10,000

Coupon rate is 4%

So by putting values, we have:

Annual Cash Inflow = $10,000 x 4% = $400