Sample MBA Math Exercises - Finance

Exercise #1: Time Value of Money with Annual Compounding
A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value. If interest rates are 8% how much would you pay today for a zero coupon bond with a face value of $2,300 that matures in 7 years?

Solution Commentary (4:30) Variable Assignments Present Value PV = ? Rate r = 0.08 Years n = 7 Future Value FV = 2,300 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 PV = FV/(1+r)n PV = 2300/1.087 PV = 1,342.03 Excel Solution Financial Calculator Solution 2,300 [FV] 0 [PMT] 8 [i] 7 [n] HIT [PV] TO SOLVE… -1342.03

Exercise #2: Time Value of Money with Semi-Annual Compounding
You deposit $500 in a bank account that pays 7% stated annual interest compounded semi-annually. What is the value of your investment at the end of 4 years?

Solution Commentary (3:45) Variable Assignments Present Value PV = 500 Rate r = 0.07 Years n = 4 Periods per Year p = 2 Future Value FV = ? 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 FV = PV*(1+(r/p))np FV = 500*(1+(0.07/2))(4*2) FV = 500*1.0358 FV = 658.40 Excel Solution Financial Calculator Solution 500 [CHS][PV] 0 [PMT] 7 [ENTER] 2 [÷][i] 4 [ENTER] 2 [×][n] HIT [FV] TO SOLVE… 658.40

Exercise #3: Constant Annuity
What is the present value of an annuity in which $300 is paid each year for 4 years, assuming a discount rate of 8% and the first payment is received one year from now?

Solution Commentary (3:57) Variable Assignments Present Value PV = ? Payment PMT = 300 Discount Rate r = 0.08 Years n = 4 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 PV = (PMT/r)[1-(1/(1+r)n)] PV = (300/0.08)[1-(1/(1+0.08)4)] PV = 3,750.00*[1-(1/1.084)] PV = 3,750.00*[1-0.74] PV = 993.64 Excel Solution Financial Calculator Solution 300 [PMT] 8 [i] 4 [n] HIT [PV] TO SOLVE… -993.64

Exercise #4: Bond
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 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-(1/1.0610.00)] 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