Question

Suppose you will go to graduate school for 2 years beginning in year 4. Tuition is $28,359 per year, due at the end of each school year. What is the Macaulay duration (in years) of your grad school tuitions? Assume a flat yield curve of 0.06. Assume annual compounding. In the above description, if you see a flat yield curve of 0.08 for example, then it means that the yield at all maturities is 8%.

Answer 1

The following cash flows are expected over the years 4 and 5:

Period 4 : $28,359

Period 5: $28,359

Period 4 Discount Factor = 1 / (1 + 6%)⁴ = 0.7921

Period 5 Discount Factor = 1 / (1 + 6%)⁵ = 0.7473

Next, multiply the period's cash flow by the period number and by its corresponding discount factor to find the present value of the cash flow:

Period 4 = 4 x $28,359 x 0.7921 = $89,851.94

Period 5 = 5 x $28,359 x 0.7473 = $105,957.47

Sum of these values = $195,809.41 = numerator

Current Bond Price = Sum of PV CFs = denominator

= [$28,359 x 0.7921] + [$28,359 * 0.7473]

= $22,462.98 + $21,191.49 = $43,654.48

Macaulay Duration = $195,809.41 / $43,654.48 = 4.49 years