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ECMA06_Tutorial_8_Solution.doc
ECMA06_Tutorial_8_Solution.doc

ECMA06_Tutorial_8_Solution.doc

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University of Toronto Scarborough

Economics for Management Studies

MGEA06H3

Iris Au

Summer

Description

ECMA06 Tutorial #8 Answer Key
Question 1
Suppose the interest rate is 10%:
Part (a)
• If you have $1000 today, after 4 years you will have:
4
$1000(1 + 0.1) = $1464.10
Part (b)
• If you are promised $8000 in 8 years, then the value of promise today, $X:
8
$8000 = $X(1 + 0.1)
$X = $8000/(1 + 0.1) = $3732.06
Question 2
Part (a)
• This is a standard bone with a face value of $100, a coupon rate of 12% and matures in 3
years.
Part (b)
If the current interest rate is 12%, the price of the bond is:
n
∑ Payment t $12 $12 $112
PDV = t 1 (1 + r)t = (1 + 0.12 )1 + 1 + 0.12 )2 + (1 + 0.12 )3 = $100
• Since the current interest rate is the same as the coupon rate, the bond will sell at par (i.e., at
its face value).
Part (c)
If the current interest rate is 10%, the price of the bond is:
n Payment $12 $12 $112
∑ t 1 2 3
PDV = t 1 (1 + r)t = (1 + 0.10 ) + 1 + 0.10 ) + (1 + 0.10 ) = $104.97
• Since the current interest rate is less than the coupon rate, the bond will sell at a premium
(i.e., above its face value).
Part (d)
If the current interest rate is 15%, the price of the bond is:
n Payment $12 $12 $112
PDV = ∑ t t = 1 + 2 + 3 = $93.15
t 1 (1 + r) (1 + 0.15 ) 1 + 0.15 ) (1 + 0.15 )
• Since the current interest rate is less than the coupon rate, the bond will sell at a discount
(i.e., below its face value).
Part (e)
If the bond sells for $120, then the current interest rate:
ECMA06 Tutorial #8 Answer Key 1 $12 $12 $112
$120 = (1 + r)1 + 1 + r ) + (1 + r)3
• Since the bond is selling at a premium, we know that the current interest rate must be lower
than the coupon rate (i.e., r < 12%).
• Let’s try using different interest rates:
r = 10% r = 8% r = 6% r = 5% r = 4%
PDV (bond price) $104.97 $110.31 $116.04 $119.06 $122.20
Note: A third-order equation is hard to solve, so we will use a method of linear approximation to
solve for the current interest rate.
⇒ From the above table, we observe that when r = 5% the PDV is closest to $120.
⇒ Also, when r falls from

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