Question

Compute the present values of the following bond using three (3) different discount rates.


Face Value = $1,000
Coupon rate = 14%

Maturity is 4 years
Coupons are paid once in a year.

Compute the PV of the bond using:
Discount rate of 16%
Discount rate of 14%
Discount rate of 12%
Discuss the relationship between PV of a bond and different discount rates.

Answer 1

Given Coupon rate is 14%

Maturity is 4 years .

Copouns are paid once in a year.

Here copoun payment are in the form of annuity

Annual copoun payments is 1000 * 14% = 140

We know the formula for present value of annuity is

Present value of annuity - P*((1-(1+r)^-n)/r

Here P is the copoun payments

r = discount rate and n = number of copouns

The formula for present value is A/(1+r)ⁿ

Where A is the Future cash inflow r = rate of interest and n = number of years from present

When discount rate is 16%

Present value = 140* (1-(1.16)^-4/0.16) + 1000/1.16⁴

140 * 0.447709/0.16 + 1000/1.810639

= 391.7453 + 552.2911

= 944.0364

When discount rate is 14%

Present value = 140* (1-(1.14)^-4/0.14) + 1000/1.14⁴

140* 0.40792/0.14 + 592.0803

= 1000

When the present value is 12%

Present value = 140* (1-(1.12)^-4/0.12) + 1000/1.12⁴

140 * 0.364482/0.12 + 635.5181

425.2289 + 635.5181

= 1060.747.

Here we can observe that when ever the discount rates are falling the present value of bonds is increasing and vice versa . This is because the lower with the denominator we divide the higher the value. When the discount rates reduces the denominator factor also reduces and hence increasing the present value