when start a new business, it needs to calculate how much profit a company would earn. In doing so, it is important to consider "time value money" and some uncertainty factors. Thus return on capital investment should not only rely on rate of return and/or payback.

1. Capital Investment Decision
ROI/Payback/DCF

2. Profit
Interest rate
Inflation
Time value of money
What do change it?
Video 2.4.1.4

3. Present value = PV
$10,000
0 1 2 3
Interest rate = 10%
FVFVFV
10,000 + (10,000 x 0.1)
=11,000
11,000 + (11,000 x 0.1)
=12,100
12,100 + (12,100 x 0.1)
=13,310FV1 = 10000 (1+0.1)
FV2 = 10000 (1+0.1) (1+0.1) (1+0.1) FV = PV (1+Interest)x(1+interest)x(1+interest)
FV = PV (1+Interest)3
FV2 = 10000 (1+0.1) (1+0.1)
Time value of money

4. How to appraise capital
investment?

5. Project Investment Profit
A 100,000 10,000
B 120,000 12,000
C 6,000 6,00
Project Investment Profit % profit
A 100,000 10000 10% = (profit/investment)x100
B 120,000 12,000 10%
C 6,000 600 10%
Which project will you choose? Why?
Which profit will you use?
Appraisal for capital investment 1

6. Battery Company…..
100,000 ? ? ? 20,000
5000 10000 15000 15000 5,000
? ? ? ? ?
Investment
Production
Profit Selling price: 12$/ Total cost: 8$
Appraisal for capital investment1

7. Year Investment
At the
beginning of
the Yr
Depreciation Investment
at the end of
the Yr
Average
investment
(B+C)/2
A B C D E
1 100,000 16,000 84,000 92,000
2 84,000 16,000 68,000 76,000
3 68,000 16,000 52,000 60,000
4 52,000 16,000 36,000 44,000
5 36,000 16,000 20,000 28,000
Investment
Annual net profit
Year # units
produced
Revenue-
(12$xF)
Total cost
(8$ x F)
Profit
(G –H)
Net profit=
profit - expense
A F G H I J
1 5,000 60,000 40,000 20,000 4,000
2 10,000 120,000 80,000 40,000 24,000
3 15,000 180,000 120,000 60,000 44,000
4 15,000 180,000 120,000 60,000 44,000
5 5,000 60,000 40,000 20,000 4,000
Appraisal for capital investment1: Rate of return

8. Year Investment
At the
beginning
of the Yr
Depreciat
;
Investme
nt at the
end of
the Yr
Average
investment
(B+C)/2
# units
produced -
Revenue-
(12$xF)
Total cost
(8$ x F)
Profit
(G –H)
Profit
from
Income
statement
(I-C)
Return
rate %
(J/E)x100
A B C D E F G H I J K
1 100,000 16,000 84,000 92,000 5,000 60,000 40,000 20,000 4,000 4%
2 84,000 16,000 68,000 76,000 10,000 120,000 80,000 40,000 24,000 29%
3 68,000 16,000 52,000 60,000 15,000 180,000 120,000 60,000 44,000 65%
4 52,000 16,000 36,000 44,000 15,000 180,000 120,000 60,000 44,000 85%
5 36,000 16,000 20,000 28,000 5,000 60,000 40,000 20,000 4,000 11%
39%
39%(J/5)/(E/5) x 100Average annual profit/Average investment x 100=
Appraisal for capital investment 1: Rate of return

9. A (000) B (000) C (000)
Start Machine cost (160) (160) (160)
Y1 Net profit after dep 20 10 160
Y2 Net profit after dep 40 10 10
Y3 Net profit after dep 60 10 10
Y4 Net profit after dep 60 10 10
Y5 Net profit after dep 20 160 10
ARR ? ? ?
Project A’s ARR = 50%/ Project B’s ARR = 50%/ Project C’s ARR = 50%
ARR ≠ Time value money
Appraisal for capital investment: Average Rate of return or Accounting RR
ARR ≠ Cash-flow
What are their ARR? Which Project will you choose? Why?

10. Appraisal for capital investment 2
Investment
($10,000)
0 1 2 3
$3,000 $5,000 $7,000Cash-Flow
Year 1: +3000
Year 2: +5000
Year 3: +2000
Total: 10,000
Year 1 Year 2 Year 3
Payback period: 2.34 yr

11. A (000) B (000) C (000)
Start Machine cost (160) (160) (160)
Y1 Net profit before dep 40 10 160
Y2 Net profit before dep 40 20 10
Y3 Net profit before dep 60 40 20
Y4 Net profit before dep 80 40 40
Y5 Net profit before dep 50 160 40
PBP 3.3 yr 4.4 yr 1 yr
PBP ≠ Time value money After PBP ≠ Cash-flow
Appraisal for capital investment: payback by the business for investment
What are their ARR? Which Project will you choose? Why?
Project A’s PBP = 3.3yr/ Project B’s PBP = 4.4 Yr/ Project C’s PBP = 1 yr
Why use net profit before
depreciation instead
that after Dep?

12. Appraisal for capital investment 3
0 1 2 3
PV
Option 1
Option 2
FV
$1,000 $1,000 + Interest
Compounding factor
Compounded value
of PV
$1,000 - Interest $1,000
Discount factor:
PV of $ invested in the future
Discounted value
of one or > future cash-flow

13. $10,000
$11,000
0.1
0.1
Compounding factor
Discounting factor
0.1
0.1
0.1
0.1
$11,000
$12,100
$12,100
$13,310
$13,310
Interest rate: 0.1

14. $10,000
$15,000
Investment
Cash-flow
FV
PV
PV
= PV(1+r)n
= FV/(1+r)n
Interest rate (r) = 10% (0.1)
What is PV of the FV?
PV of the FV = $11,269
Initial Invest = $ 10,000
Net PV = $ 1,269
Timing cash-flow √
Detect +/- of wealth √
Return %? X
Rank alternatives? X
Appraising NPV
= FV x 1/(1+r)n or FV x discount rate
Appraisal for capital investment 3

15. $10,000
$6,000
$5,000
$1,000
PV of CF1
PV of CF2
PV of CF3
Discounting rate: 0.1
(interest rate 10%)
909
4,132
4,508
Total 9,549
NPV = initial investment + PV of CF1+PV of CF2+PV of CF3
NPV = initial investment + ∑ CF of year 1,2,3/(1+r)3
NPV = (-10000)+ (909+4132+4508) = -451
Appraisal for capital investment 3

17. Timing cash-flow √
Detect +/- of wealth √
Return %? X
Rank alternatives? X
NPV calculation based on market interest rate (discount rate)
but not known its actual rate of return
1000 2000
Year 0 Year 5
r =10%
PV: 1241
Rate of return>10% (r)
If PV: 1000
Rate of return?
Maybe > or < r
Rate of return
when PV of FV =initial investment
(NPV = 0)
Internal Rate of Return (IRR)
Appraisal for capital investment 4

18. IRR: discount rate when NPV is “0”.
Can we know “scale of investment” through IRR?
In the case of unconventional cash-flow….
Appraisal for capital investment 4

19. Video clip from YouTube

20. Appraisal for capital investment by using NPV & IRR
Timing cash-flow √
Detect +/- of wealth √
Return %? √
Rank alternatives? √
NVP
IRR

21. Appraisal for capital investment by using NPV & IRR

22. Methods of Capital Investment Appraisal
ARR
PBP
NPV
IRR
Neglect TVM
Emphasize TVM
Short-term business decision
Long-term business decision
Net profit
Cash-flow
Discounted CF
Discounted CF