Question

1.Assume you that today you can buy a pure discount bond for $890. The bond matures in 5 years.

What is this bonds yield to maturity (YTM)?

2.Assume you can buy a pure discount bond today at a price of $746. The bond matures in 5 years.

What would be the percentage of capital gain over the life of the bond?

Answer 1

Q1

Price of Discount Bond today (Present Value) = $890
Time period = 5 years
Discount bonds are the bonds which are issued at a discount and are redeemable at face value. Such bonds do not pay any coupon interest. The bonds have face value of $1000, $10,000 and so on.

So, Future/Face value to be received at maturity = $1000

Formula in case of discount bond
PV = FV / (1+YTM)^n or PV = FV * PVF(YTM, 5)
where PV = Present Value
FV = Future Value
YTM = Yield to Maturity
n = Time period

$890 = $1000 * PVF(YTM, 5)
0.890 = PVF(YTM, 5)

Note: PVF(YTM, 5) = 0.890 indicates Present Value factor of YTM for 5 years = 0.890.
Using Present value factor table, we will search in time period = 5 years at which rate PVF = 0.890 or close to 0.890

Rate	PVF (YTM,5)
2%	0.90573081
3%	0.86260878

This means YTM lies between 2% & 3%

Using Interpolation

YTM = 2% + (0.90573081 - 0.890) / (0.90573081 - 0.86260878)
YTM = 2% + 0.01573081 / 0.04312203
YTM = 2% + 0.3647975
YTM = 2.3647975% or 2.36% (approx).

Q 2.

Issue Price of pure discount bond today =  $746.
Maturity Period = 5 years.

Discount bonds are the bonds which are issued at a discount and are reedemable at face value. Such bonds do not pay any coupon interest. The bonds have face value of $1000, $10,000 and so on.
So, Face value or redemption value to be received at maturity = $1000

Percentage of capital gain over the life of the bond = (RV - IP) / IP *100
where RV = Redemption value  & IP = Issue Price

Percentage of capital gain over the life of the bond = ($1000 - $746) / $746 *100

= $254 / $746 *100 = 34.0483%

Percentage of capital gain over the life of the bond = 34.05%