BÀI TẬP F2 2 CHƯƠNG 5 NHÓM 4

NHÓM 4
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1 Phạm Quốc Huy 187ke19345 100%
2 Nguyễn Huyền Yến Oanh 187ke05619 100%
3 Huỳnh Thị Kim Huyền 187ke19351 100%
4 Lương Ngọc Kim Ngân 187ke19498 100%
CHAPTER 5: METHODS OF PROJECT APPRAISAL
5.6. A project requiring an investment of $1,200 is expected to generate

returns of $400 in years 1 and 2 and $350 in years 3 and 4. If the NPV =
$22 at 9% and the NPV = -$4 at 10%. What is the IRR for the project?
A 9.15%
B 9.85%
C 10.15%
D 10.85%
IRR = 9% + ( ( 22/22+4) × 1) = 9% + 0.85 = 9.85%
5.7 A sum of money was invested for 10 years at 7% per annum and is
now worth $2,000. What was the original amount invested (to the
nearest $)?
A $1,026
B $1,017
C $3.937
D $14,048
P = S/(1 + r)^n = 2000/(1+7%)^10 = $1,017
5.8 House prices rise at 2% per calendar month. What is the annual rate
of increase correct to one decimal place?
A 24%
B 26.8%
C 12.7%
D 12.2%
(1 + 2%)^12= 1.268
 1,268 – 1 = 0,268 = 26.8%
5.9 What is the present value of ten annual payment of $700, the first
paid immediately and discounted at 8%, giving your answer to the
nearest $?
A $4,697
B $1.050
C $4,435
D $5,073
Annuity factor = 1 + 6,247 = 7,247(cumulative for 9 years, first payment
is now)
PV of annuity = $700 × 7,247 = $5,073
5.10 An investor is to receive an annual of $19,260 for six years

commencing at the end of year1. It has a present value of $86,400.
What is the rate of interest (to the nearest whole a percent)?
A 4%
B 7%
C 9%
D 11%
Annuity factor = 86,400/19,260 = 4,486
1−(1+ r)−6
 4,486= r
 r = 9%
5.11 How much should be invested now (to the nearest $) to receive
$24,000 per annum in perpetuity if the annual rate of interest is 5%?
A $1,200
B $25,200
C $120,000
D $480,000
P = 24,000/5% = 480,000
5.12 The net present value of an investment at is $24,000, and at 20% is
-$8,000. What is the internal rate of return of this investment?
A 6%
B 12%
C 16%
D 18%
IRR = 12% + (24,000/24,000 + 8,000)× (20% - 12%) = 18%
State your answer to the nearest whole percent.
The following date relevant for questions 5.13 and 5.14.
Diamond Ltd has a payback period limit of three years and is
considering investing in one the following projects. Both projects
require an initial investment of $800,000. Cash inflows accrue evenly
throughout the year.
Project Alpha Project Beta
Year Cash inflow Year Cash inflow
$ $
1 250,000 1 250,000
2 250,000 2 350,000
3 400,000 3 400,000
4 300,000 4 200,000
5 200,000 5 150,000
6 50,000 6 150,000
The company’s cost of capital is 10%.
5.13 What is the non-discounted payback period of Project Beta?
A 2 years and 2 months
B 2 years and 4 months
C 2 years and 5 months
D 2 y ears and 6 months
200,000
2 years+
400,000
×12 month=2 years + 6month
5.14. What is the discounted payback period of Project Alpha ?

A. Between 1 and 2 years
B. Between 3 and 4 years
C. Between 4 and 5 years
D. Between 5 and 6 years
5.15. A capital investment project has an initial investment followed by

constant annual returns.
How is the payback period calculated ?
A. Initial investment ÷ annual profit
B. Initial investment ÷ annual net cash inflow
C. (Initial investment - residual value) ÷ annual profit
D. (Initial investment - residual value) ÷ annual net cash inflow
The payback period is the time that is required for the total of the cash
inflows of a capital investment project to equal the total of the cash
outflows, is initial investment ÷ annual net cash inflow.
5.16. A machine has an investment cost of $60,000 at time 0. The

present values (at time 0) of the expected net cash inflows from the
machine over its useful life are:
Discount Present value of
rate cash inflows
10% $64,600
15% $58,200
20% $52,100
What is the internal rate of return (IRR) of the machine investment ?
A. Below 10%
B. Between 10% and 15%
C. Between 15% and 20%
D. Over 20%
$
Investment (60,000)
PV of cash
64,600
inflow
NPV @ 10% 4,600
$
Investment (60,000)
PV of cash
58,200
inflow
NPV @ 15% (1,800)
The IRR of the machine investment is therefore between 10% and 15%
because the NPV falls from $4,600 at 10% to -$1,800 at 15%. Therefore
at some point between 10% and 15% the NPV = 0. When the NPV = 0,
the internal rate of return is reached.
5.17. An investment project has a positive net present value ( NPV ) of
$7,222 when its cash flows are discounted at the cost of capital of 10%
per annum. Net cash inflows from the project are expected to be $18,000
per annum for five years. The cumulative discount (annuity) factor for
five years at 10% is 3.791.
What is the investment at the start of the project ?
A. $61,016
B. $68,238
C. $75,460
D. $82.778
Cash Discount Present

Year
flow factor value
$ 10% $
0 x 1.000 (x)
1 - 5 18,000 3.791 68,238
7,222
-x + $68,238 = $7,222
x = $68,238 - $7,222
x = $61,016
5.18 Which of the following accurately defines the internal rate of return
(IRR)?
A. The average annual from an investment expressed as a percentage of
the investment sum
B. The discount rate (%) at which the net present value of the cash flows
from an investment is zero
C. The net present value of the cash flows an investment discounted at
the required rate of return
D. The rate (%) at which discounted net profits from an investment are
zero
5.19 An investment project has the following discounted cash flows
($’000):
Year Discount rate
0% 10% 20%
0 (90) (90) (90)
1 30 27.3 25.0
2 30 24.8 29.8
3 30 22.5 17.4
4 30 20.5 14.5
30 5.1 (12.3)
The required rate of return on investment is 10% per annum.
What is the discounted payback period of investment project?
A. Less than 3.0 years
B. 3.0 years
C. Between 3.0 years and 4.0 years
D. More than 4.0 years
At the end of year 3, $74,600 has been 'pay back'. The remaining
$15,400 for payback will be received during year 4.
5.20 What is the effective annual rate of interest of 2.1% compounded
every three months?
A. 6.43%
B. 8.40%
C. 8.67%
D. 10.87%
(1 + 2.1%)^4 = 8.67%
5.21 If the interest rate is 8% what would for a perpetuity of $1,500
starting in one year’s time (to the nearest $)
A. $1,620
B. $17,130
C. $18,750
D. $ 20,370
PV = a/r = 1,500/8% = $18.750
5.22 The following question is taken from the June 2012 exam paper.
An investor has the choice between two investments. Investment Exe
offers interest of 4% per year compounded semi-annually for a period of
three years. Investment Wye offers one interest payment of 20% at the
end of its four-year life.
What is the annual effective interest rate offered by the two investments?
Investment Exe Investment Wye
A. 4.00% 4.66%
B. 4.00% 5.00%
C. 4.04% 4.66%
D. 4.04% 5.005
(1 + 2%)^2 – 1 =4.04%
(1 + 25%)^2 – 1 = 4.66%
5.23 The following question is taken from the June 2013 exam paper.
A project has an initial outflow of $12,000 followed by six equal annual
cash inflows, commencing in one year’s time. The payback period is
exactly four years. The cost of capital is 12% per year.
What is the project’s net present value (to the nearest $)?
A. $333
B. -$2,899
C. -$3,778
D. -$5,926
$12,000 ÷ 4 years = $3,000 per year
-$12,000 + 4.111 x $3,000 = $333

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NHÓM 4

STT Tên MSSV Hoàn thành

CHAPTER 5: METHODS OF PROJECT APPRAISAL

5.6. A project requiring an investment of $1,200 is expected to generate

5.10 An investor is to receive an annual of $19,260 for six years

5.14. What is the discounted payback period of Project Alpha ?

5.15. A capital investment project has an initial investment followed by

5.16. A machine has an investment cost of $60,000 at time 0. The

Cash Discount Present

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