Exercise 1 Sensitivity Analysis Muhammad Arif Naufal
18522032
An alternative investment is estimated to require an initial funding of Rp 10,000,000.00 with zero salvage value at the end of the fifth year. Annual income is estimated at Rp. 3,000,000.00.
The company sets MARR of 12%. Make a sensitivity analysis by changing the value:
a. Interest rate (12% - 15%), when the other parameters remain the same.
b. Initial investment (IDR 6,000,000.00 - IDR 10,000,000.00), when the other parameters remain the same.
Set up the PW relation for 5 years, when i = 12%
PW = -Rp10.000.000 + Rp3.000.000 (P/A, 12%,5) PW = -Rp10.000.000 + Rp3.000.000 (3,6048) PW = Rp814.400
Set up the PW relation for 5 years, when i = 13%
PW = -Rp10.000.000 + Rp3.000.000 (P/A, 13%,5) PW = -Rp10.000.000 + Rp3.000.000 (3,5189) PW = Rp556.700
Set up the PW relation for 5 years, when i = 14%
PW = -Rp10.000.000 + Rp3.000.000 (P/A, 14%,5) PW = -Rp10.000.000 + Rp3.000.000 (3,4331) PW = Rp299.300
Set up the PW relation for 5 years, when i = 15%
PW = -Rp10.000.000 + Rp3.000.000 (P/A, 15%,5) PW = -Rp10.000.000 + Rp3.000.000 (3,3522) PW = Rp56.600
1% increment
i PW
12% 814.400,00
13% 556.700,00
14% 299.300,00
15% 56.600,00
1 2 3 4
0%
10000000%
20000000%
30000000%
40000000%
50000000%
60000000%
70000000%
80000000%
90000000%
i PW
The PW measure is positive for all values of i, so the decision to invest is not materially affected by the interest rate.
Select Rp2.000.000 increment to evaluate sensitivity
Set up the PW relation for 5 years, when i = 12%, P = Rp10.000.000 PW = -Rp10.000.000 + Rp3.000.000 (P/A, 12%,5)
PW = -Rp10.000.000 + Rp3.000.000 (3,6048) PW = Rp814.400
Set up the PW relation for 5 years, when i = 12%, P = Rp8.000.000 PW = -Rp8.000.000 + Rp3.000.000 (P/A, 12%,5)
PW = -Rp8.000.000 + Rp3.000.000 (3,6048) PW = Rp2.814.400
Set up the PW relation for 5 years, when i = 12%, P = Rp6.000.000 PW = -Rp6.000.000 + Rp3.000.000 (P/A, 12%,5)
PW = -Rp6.000.000 + Rp3.000.000 (3,6048) PW = Rp2.814.400
Initial investment PW
Rp10.000.000 Rp814.400,00 Rp8.000.000 Rp2.814.400,00 Rp6.000.000 Rp4.814.400,00
1 2 3 Rp0
Rp2,000,000 Rp4,000,000 Rp6,000,000 Rp8,000,000 Rp10,000,000 Rp12,000,000
Initial investment PW
The PW measure is positive for all values of initial investment, so the decision to invest is not materially affected by the initial investment.
Exercise 2 Payback Period
ABB purchased fieldbus communication equipment for a project in South Africa for $3.15 million. The net cash flow is estimated at $500,000 per year, and a salvage value of $400,000 is anticipated regardless of when it is sold. Determine the number of years the equipment must be used to obtain payback at MARR values of 0% and 8%
P = $3.15 millions A = $ 0.5 million/year F = $ 0.4 millions i = 0%
0 = -$3.15 + $0.5 (n) + $0.4 n = 5.5 year
i = 8% (discounted payback)
0 = -$3.15 + $0.5 (P/A,8%,n) + $0.4(P/F,8%,n)
n (year) PW ($, million)
12 0.77689
10 0.39033
X 0
8 -0.06058
X = 8 + [(0-(-0.06058))/( 0.77689-(-0.06058)] (2) X = 8 + (0.1343)x(2)
X = 8 + 0.2686
X = 8.2686 ≈ 8.3 years