QBM case study

Quantitative Business Methods

Problem 1.
A client invests $500,000 in a bond fund project to earn 7% annually. Estimate the value of this investment after 10 years.
Solution
FVN = PV(1+r)N
Here we have FV10= 500,000 (1+0,07)10 = 983 575,68
Problem 2.
For liquidity purposes a client keeps $100,000 in a bank account. The bank quotes a stated annual interest rate of 7%. How much will your client have in this account at the end
a. One year
b. Two years
Assuming no withdrawals (so all the interest are reinvested) with
1. Quarterly compounding
2. Monthly compounding
3. Continuous compounding
Solution
a. One year investment
1. Quarterly compounding
FVN = PV(1+r/m)mN
FVN = 100,000(1+0,07/4)4x1=107 185,90
2. Monthly compounding
FVN = PV(1+r/m)mN
FVN = 100,000(1+0,07/12)12x1=107 229,01
3. Contiuous compounding
FVN = PVer
FVN = 100,000(e)0,07=107 250,82

b. Two years
4. Quarterly compounding
FVN = PV(1+r/m)mN
FVN = 100,000(1+0,07/4)4x2=114 888,18
2012

Quantitative Business Methods

5. Monthly compounding
FVN = PV(1+r/m)mN
FVN = 100,000(1+0,07/12)12x2=114 980,60
6. Contiuous compounding
FVN = PVer
FVN = 100,000(e)0,07x2=115 027,38
Problem 3.
A couple plans to set aside $20,000 per year in a portfolio that earns 7% a year. If they make their first saving contribution one year from now, how much will they have at the end of 20 years? Solution

 (1  0,07) 20  1 
  819909,84
PV  20000


0,07



Problem 4.
To cover the first year’s total college tuition payments for his two children, a father will make a
$75,000 payment five years from now. How much will he need to invest today to meet this payment if the investment earns 6% annually?
Solution
 75000 
PV  
 (1  0,06) 5   56044,36




Problem 5
Two major investment projects each have the same initial capital outlay of $2,000 million. The expected net revenues on the respective projects over the next 4 years are