PORTFOLIO OF EXERCISES | 2nd GRADED EXERCISE | MATHEMATICS OF FINANCE
Question 1: An investor is presented with alternative projects, A and B, with the following end-of-year cash flows. Each project requires an investment of $150,000.
Year 1 2 3 4
Project A $75,000 $65,000 $55,000 $30,000
Project B $25,000 $25,000 $35,000 $145,000
A. Using the net present value (NPV) capital budgeting model, which project should be chosen if the cost of capital is 6% interest compounded annually? (5 points)
Project A:
-150,000 + (75,000/1+6%) + (65,000/1+6%)2 +(55,000/1+6%)3 + (30,000/1+6%)4=
-150,000 + 70,754.71 + 57,849.76 + 46,179.06 + 23762.80= $48,546.33
Project B:
-150,000 + (25,000/1+6%) + (25,000/1+6%)2 + (35,000/1+6%)3 + (145,000/1+6%)4=
-150,000 + 23,584.9 + 22,249.91 + 29,386.67 + 114,853.58= $40,075.06
It should be chosen project A.
B. Using the net present value (NPV) capital budgeting model, which project should be chosen if the cost of capital is 8.5% interest compounded annually? (5 points)
Project A:
-150,000 + (75,000/1+8.5%) + (65,000/1+8.5%)2 + (55,000/1+8.5%)3 + (30,000/1+8.5%)4=
-150,000 + 69,124.42 + 55,214.59 + 43,059.94 + 21,647.22= $39,046.17
Project B:
-150,000 + (25,000/1+8.5%) + (25,000/1+8.5%)2 + (35,000/1+8.5%)3 + (145,000/1+8.5%)4=
-150,000 + 23,041.47 + 21,236.38 + 27,401.78 + 104,628.27= $26,307.9
It should be chosen project A.
Question 2:
A. Define perpetuity and discuss one example of a perpetuity. (5 points)
An annuity whose payments begin on a fixed date and continue forever.
Ex. Find the discounted value of an ordinary simple perpetuity paying $80 a month, if j12=10%.
PV= R/i= 80/0.0083=$9638.55
B. Calculate the present value of an ordinary simple perpetuity paying $100 a month if the annual compounded interest rate is 9%. (5 points)
PV=R/i= 100/0.09= $1111.11
Question 3:
A. Define both an annuity due and an ordinary annuity. What is the key difference between the two? (5 points)
Annuity due: Annuity whose periodic payment is due at the beginning of each payment interval.
Ordinary annuity: Annuity whose first payment is due sometimes after the end of the first interest period.
The key difference between both is that Annuity due is at the beginning of each period and Ordinary annuity is at the end of each period.
B. What will the ending balance be in an ordinary annuity if you were to invest $500 in an investment every year for 6 years at an interest rate of 6.5% compounded annually? (5 points)
PP=$500
j=6.5%=0.065
t=6 year
k= 1 year
PV=500[1-(1+ 0,0651) -6 ]0,0651 (1+ 0,0651)-1
PV=$2272.77
C. What will the ending balance be in an annuity due be if you were to invest $500 in an investment every year for 6 years at an interest rate of 6.5% compounded annually? (5 points)
PP=$500
r=6.5%=0.065
t=6
m=1
FV=500[(1+ 0,0651) (1)(6) −1]0,0651 (1+ 0,0651)
FV= $3,761.43
D. What is the present value of an ordinary annuity if the annuity pays $600 a year, for 5 years, at a compounded interest rate of 6.5%? (5 points)
PP=$600
j=6.5%=0.065
t=5
k=1
PV=600[1-(1+ 0,0651) -5 ]0,0651 (1+ 0,0651) -1
PV=$2341.22
