Class Notes (785,637)
MGEA06H3 (150)
Iris Au (138)
Lecture

# ECMA06_Tutorial_8_Solution.doc ECMA06_Tutorial_8_Solution.doc

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School
University of Toronto Scarborough
Department
Economics for Management Studies
Course
MGEA06H3
Professor
Iris Au
Semester
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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