Question

Let’s suppose today is 1/4/2019 and you observe the information from various coupon bonds issued by

the Australian Government. Using the bond information, please complete the following tasks:

Suppose that there is a risk-free investment which pays $10,000, $20,000, $30,000, $40,000, and

$50,000 at the beginning of April each year for the next 5 years. How much will you pay for the

investment?

Maturity Date	CR (%)	Price	FV	Freq
2020/4/1	4.50	$103.09	$100.00	Annual
2021/4/1	5.75	$108.94	$100.00	Annual
2022/4/1	2.25	$102.97	$100.00	Annual
2023/4/1	5.50	$116.13	$100.00	Annual
2024/4/1	2.75	$106.25	$100.00	Annual

Answer 1

First, we calculate the YTM of each bond with maturities from 1 to 5 years.

YTM is calculated using the RATE function in Excel with these inputs :

nper = number of years to maturity

pmt = face value * CR

pv = -price (this is a negative figure since it represents a cash outflow to the buyer of the bond)

fv = face value

YTM of the 1-year bond is 0.58%

YTM of the 2-year bond is 1.20%

YTM of the 3-year bond is 1.24%

YTM of the 4-year bond is 1.33%

YTM of the 5-year bond is 1.45%

Present worth of the risk-free investment is calculated as :

($10,000 * (1 + 0.0058)) + ($20,000 * (1 + 0.0120)²) + ($30,000 * (1 + 0.0124)³) + ($40,000 * (1 + 0.0133)⁴) + ($50,000 * (1 + 0.0145)⁵)

present worth = $157,559.91