Question

In: Accounting

XYZ limited had issued bonds with a par value of Rs. 100 and a coupon rate...

XYZ limited had issued bonds with a par value of Rs. 100 and a coupon rate of 12% p.a. The bond has maturity of 30 months and pays quarterly coupons. Calculate the fair price of the bond if the required rate of return by investors is 8%.

Expert Solution

Fair Price of Bond Calculation

Step 1: Calculate the coupon payment and number of payments.

Since the payment will be made quarterly,

Coupon amount = 12% of 100 (1/4)

= $3

Number of coupon payments (n) = 10

(because there are 30 months & quarter has 3 months, number of coupon payments = 30/3)

Step 2: Calculate the quarterly required rate of return.

Yearly rate of return = 8%

Quarterly rate of return (r) = 2%

(8% divided by 4)

Step 3: Calculation of fair price of the bond shall be the present value of future payments.

Present Value = Coupon Payment * Present value of Annuity Factor_(r,n) + Par Value * Present Value Factor _(r,n)

= $3 * PVAF_(r,n) + 100 * PVF _(r,n)

= $3 * PVAF_(2%,10) + 100 * PVF _(2%,10)

= $3 * 8.98258 + 100 * 0.8203482

= 26.94774 + 82.03482

= $108.98

Fair Price of the Bond shall be $108.98

Explanatory Notes:

1. PVAF can be calculated by the following formula:

[1 - (1+r) ^-n] / r

where n is the number of coupon payments & r is the required rate of interest

2. PVF can be calculated by the following formula:

1/ (1+r) ⁿ

where n is the number of coupon payments & r is the required rate of interest

ekkarill92 answered 1 year ago

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