TUTORIAL 11
BUSINESS MATHEMATICS
MARCH 2003
Note
how the terms market rate and discount rate are used for interest rate.
1.)
An
investment proposal requires an initial capital outlay of $10,000 and will
produce a return of $12,500 at the end of five years Use the following methods
to decide if this investment is worthwhile, given a market rate of 15%
compounded annually:
a.)
Net
Present Value
b.)
Internal
Rate of Return
2.)
Find
the Net Present Value for the following cash flows given a minimum interest
rate of 10%.
|
Year |
Cash Flows |
|
0 |
-1,300,000 |
|
1 |
360,000 |
|
2 |
400,000 |
|
3 |
350,000 |
|
4 |
500,000 |
3.)
The
estimated net cash flows of a project are as follows:
|
Year |
0 |
1 |
2 |
3 |
4 |
5 |
|
Net Cash Flows |
-1,000,000 |
0 |
250,000 |
550,000 |
500,000 |
400,000 |
Calculate
the NPV of the investment, using a discount rate of 10%
4.)
A firm
must select either Project A or Project B. Project A requires an initial outlay
of RM27,000 and yields RM29,500 at the end of two years. Project B requires an
initial outlay of RM18,000 and yields RM20,000 at the end of 2 years. Which project should the firm
choose?
5.)
A
project that which requires an initial outlay of RM10,000 produces a return of
RM4,000 at the end of Year 1 and RM8,000 at the end of Year 2
a.)
Find
the NPV when the interest rate is 10%
b.)
Find
the NPV when the interest rate is 12%
c.)
Find
the IRR
6.)
Estimate
the IRR for Project A and Project B, given the following information:
Project
A:
Discount
rate of 15% yields NPV of $12,000
Discount
rate of 18% yields NPV of -$6,000
Project
B:
Discount
rate of 12% yields NPV of $15,000
Discount
rate of 16% yields NPV of -$4,000
If
you had to choose only one of these, which one would you choose? Why?
7.)
A
company is considering launching either Product A or Product B. The estimated
revenues and costs (in RM) for these products over the next five years is as
follows. Assume revenues represent net cash inflows and costs represent net
cash outflows
Product A:
|
Year |
0 |
1 |
2 |
3 |
4 |
5 |
|
Revenues |
90,000 |
36,000 |
50,000 |
75,000 |
80,000 |
90,000 |
|
Costs |
180,000 |
18,000 |
30,000 |
50,000 |
42,000 |
45,000 |
|
|
|
|
|
|
|
|
Product B:
|
Year |
0 |
1 |
2 |
3 |
4 |
5 |
|
Revenues |
90,000 |
50,000 |
80,000 |
100,000 |
120,000 |
90,000 |
|
Costs |
220,000 |
20,000 |
30,000 |
50,000 |
70,000 |
75,000 |
|
|
|
|
|
|
|
|
a.)
Find
the NPV using an interest rate of 12%. Which project is better?
b.)
Find the
NPV using an interest rate of 18% and use the results to estimate an IRR for
each project. Based on the IRR, which project is preferable?
Hint: First calculate the Net Cash Flows (revenues minus costs)
8.)
Two
projects have the following cash flows:
Project A:
|
Year |
0 |
1 |
2 |
3 |
|
Revenues |
- |
50,000 |
60,000 |
70,000 |
|
Costs |
28,000 |
40,000 |
45,000 |
50,000 |
|
|
|
|
|
|
Project B:
|
Year |
0 |
1 |
2 |
3 |
|
Revenues |
- |
60,000 |
70,000 |
80,000 |
|
Costs |
37,000 |
48,000 |
52,000 |
56,000 |
|
|
|
|
|
|
a.)
Find
the NPV using an interest rate of 15%.
b.)
Find
the NPV using an interest rate of 26% and use the results to estimate an IRR
for each project. Based on the IRR, which project is preferable?
Independent study: FRA Chapter 22
