Questions from Part D. Chapter 10. Project Appraisal and risk.
Exercise 1.
1) Sensivity analysis
A company has a cost of capital of 10%. Project A has the following present values.
Initial investment
Cash Inflows
Cash Outflows
$
300 000
600 000
100 000
What is the sensitivity of Project A to changes in the cash inflows?
A) 33%
B) 40%
C) 67%
D) 300%
Solution: NPV = –300,000 + 600,000 – 100,000 = 200,000
Sensivity=200 000/600 000*100=33%
Exercise 2. Test your understanding 1 on Sensitivity analysis
An investment of $40,000 today is expected to give rise to annual contribution of $25,000.
This is based on selling one product, with a sales volume of 10,000 units, selling price of
$12.50 and variable costs per unit of $10. Annual fixed cost of $10,000 will be incurred for
the next four years; the discount rate is 10%.
Required:
(a)Calculate the NPV of this investment.
(b)Calculate the sensitivity of your calculation to the following:
(i)initial investment
(ii) selling price per unit
(iii)sales volume
(iv)fixed costs
(v) discount rate
Exercise 3. Test your understanding on Sensitivity analysis
•
Bacher Co is considering investing $500,000 in equipment to produce a new type of ball.
Sales of the product are expected to continue for three years, at the end of which the
equipment will have a scrap value of $80,000. Sales revenue of $600,000 pa will be
generated at a variable cost of $350,000. Annual fixed costs will increase by $40,000.
(a) Determine whether, on the basis of the estimates given, the project should be undertaken,
assuming that all cash flows occur at annual intervals and that Bacher Co has a cost of capital of 15%.
(b) Find the percentage changes required in the following estimates for the investment decision to
change:
•
(i)initial investment
•
(ii) scrap value
•
(iii)selling price
•
(iv)unit variable cost
•
(v) annual fixed cost
•
(vi)sales volume
•
(vii) cost of capita
2) Probability analysis
Exercise 1. A firm has to choose between three mutually exclusive projects, the outcomes of
which depend on the state of the economy.
The following estimates have been made:
State of the economy
Recession
Stable
Growing
0,5
0,4
0,1
NPV
NPV
NPV
($0000)
($000)
($0000)
Probability
Project A
100
200
1400
Project B
0
500
600
Project C
180
190
200
Determine which project should be selected on the basis of expected market values.
Solution: Project A: 0.5*100+0.4*200+0.1*1400=270
Project B: 0.5*0+0.4*500+0.1*600=260
Project C: 0.5*180+0.4*190+0.1*200=186
Project A has the highest expected value
3) Risk adjusted discount rates
Exercise 1.
The cash flows are the first discounted using an appropiate discount rate that reflects the risk
profile of the project. The cumulative discounted cash flows need to be calculated.
A project with the following cash flows is under consideration.
T0
T1
T2
T3
T4
(20000)
8000
12000
4000
2000
Cost of capital 8%.
Required: Calculate the discounted payback period
Solution:
Year
Working
0
Discounted
cash flow
Cumulative
discounted
cash flow
-20000
-20000
1
8000/(1.08)^1
7407
12593
2
12000/(1.08)^2
10288
2305
3
4000/(1.08)^3
3175
870
Following the table on the right below, the discounted
payback period=2 years+(2305/3175)=2.73 years
Exercise 2.
A company is currently evaluating a project which requires investments of $12 000 now, and $4
800 at the end of year 1. The cash inflow from the project will be $16 800 at the end of year 2
and $14 400 at the end of year 3. The cost of capital is 15%.
What is the discounted payback period (DPP) and the net present value (NPV)?
Exercise 3.
Tele Co has divisions, and they are allowed to make their own investment decisions subject to confirmation by
the main company board. Because each of the three divisions (X, Y and Z) are subject to different levels of risk,
it has been thought appropriate to use different discount rates in each division.
X has been told that its real discount rate is 6%. The general rate of inflation, based on an index that uses a very
wide range of prices, is 3%. In the industry in which X operates, a number of prices are seen to be inflating at
4%.
Y is assessing a project in which the first of five annual lease payments has been agreed at 100,000 Som (KGS).
This is payable in one year’s time and subsequent payments will rise by 5% per annum. Y’s money cost of
capital is 8%.
Z is considering investing 900,000 KGS in a project which will produce the following annual outflows and
inflows.
Year
Outflows (000 KGS)
Inflows (000 KGS)
1
1,500
1,750
2
2,000
2,500
3
1,000
1,500
The cash flows, which arise at the end of each year, are stated in current year terms. It is expected that outflows
will rise by 4% per annum and inflows by 3% per annum. The money cost of capital of the Z Division is 10%.
(1) What is X’s money discount rate?
A) 9.1%
B) 4.0%
C) 10.24%
D) 1.1%
2) What is the present value of Z’s project’s 1 st year net cash flows (to the nearest ‘000 KGS)?
A) 220,000 KGS
B) 227,000 KGS
C) 250,000 KGS
D) 240,000 KGS
3) When considering risk in project appraisal, what is the main advantage of using simulations to assist the
appraisal?
A) A clear decision tree rule
B) More than one variable can change at a time
C) Mathematically more accurate than other methods
D) Graphical model is easier to understand
4) Is it possible to have a negative real discount rate to apply to the cash flow estimates made in current
terms when making investment decisions?
From the below, select yes or no and then select your reason
Answer:
Yes
No
Reason:
A) The calculation of a present value won’t work if the discount rate is negative
B) Negative interest rates never happen in the real world
C) It will happen if the rate of inflation exceeds the money cost of capital
A) Yes, A;
B) No, C
C) Yes, A and B;
D) Yes, C
Section B:
#
Answer
Explanation
Points
1
A
Answer=1.06*1.03-1=9.1%
5
2
A
(1,750*1.03-1,500*1.04)/1.10=220,000
5
3
B
4
D
Total:
5
Yes, It will happen if the rate of inflation
exceeds the money cost of capital
5
20 points