MBA Math Sample Exercise

Finance: Bond Present Value

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Exercise

What is the current value of a $1,000 bond with a 10% annual coupon rate (paid semi-annually) that matures in 5 years if the appropriate stated annual discount rate is 12%?

Solution

Solution Commentary

(3:29)

Variable Assignments

Present Value PV = ?
Rate r = 0.12
Years n = 5
Periods per Year p = 2
Future Value FV = 1,000
Coupon Rate = 0.10

Cash Flow

By convention for charting, Present Values are depicted as negative, reflecting an initial investment outflow in return for future cash inflows.

Manual Solution

We must separate the present value calculations for the interest payment annuity and the face value.

PV of interest annuity = (PMT/(r/p))[1-(1/(1+(r/p))^n*p)]

PV of interest annuity = (50/(0.12/2))[1-(1/(1+(0.12/2))^5*2)]

PV of interest annuity = 833.33*[1-(1/1.06^10.00)]

PV of interest annuity = 833.33*[1-0.56]

PV of interest annuity = 368.00

PV of face value = FV/(1+(r/p))^np

PV of face value = 1000/(1+(0.12/2))^(5*2)

PV of face value = 1000/1.060¹⁰

PV of face value = 558.39

PV of Bond = 926.40

Excel Solution

Financial Calculator Solution

1,000	[FV]
50	[PMT]
6	[i]
10	[n]
HIT [PV] TO SOLVE…	-926.40

Peter Regan teaches decision science courses at Dartmouth’s Tuck School and Duke’s Fuqua School. He also teaches pre-term quantitative skills courses at Tuck and Cornell’s Johnson School. He created the MBA Math self-paced, online pre-MBA quantitative skills course covering finance, accounting, economics, statistics, and spreadsheets.