Solutions to week 5 Tutorial Questions
*************** Part I: Duration Models **************
1.
What are the two different general interpretations of the concept of duration, and what is
the technical definition of this term? How does duration differ from maturity?
Duration measures the weighted-average life of an asset or liability in economic terms. As such,
duration has economic meaning as the interest sensitivity (or interest elasticity) of an asset’s
value to changes in the interest rate. Duration differs from maturity as a measure of interest rate
sensitivity because duration takes into account the time of arrival and the rate of reinvestment of
all cash flows during the assets life. Technically, duration is the weighted-average time to
maturity using the relative present values of the cash flows as the weights.
2. A one-year, $100,000 loan carries a coupon rate and a market interest rate of 12 percent.
The
loan requires payment of accrued interest and one-half of the principal at the end of six months.
The remaining principal and accrued interest are due at the end of the year.
a.
What will be the cash flows at the end of six months and at the end of the year?
CF
1/2
= ($100,000 x .12 x ½) + $50,000 = $56,000 interest and principal.
CF
1
= ($50,000 x .12 x ½) + $50,000 = $53,000 interest and principal.
b. What is the present value of each cash flow discounted at the market rate?
What is the
total present value?
PV of CF
1/2
= $56,000
1.06
=
$52,830.19
PV of CF
1
=
$53,000
(1.06)
2
=
47,169.81
PV Total CF
= $100,000.00
c. What proportion of the total present value of cash flows occurs at the end of 6 months?
What proportion occurs at the end of the year?
X
1/2
= $52,830.19
$100,000 = .5283 = 52.83%
X
1
= $47,169.81
$100,000 = .4717 = 47.17%
d. What is the duration of this loan?
Duration = .5283(1/2) + .4717(1) = .7358
OR
t
CF
PVof CF
PV of CF x t
½
$56,000
$52,830.19
$26,415.09
1
53,000
47,169.81
47,169.81
$100,000.00
$73,584.91