Garage, Inc., has identified the following two mutually exclusive projects: What
ID: 2748927 • Letter: G
Question
Garage, Inc., has identified the following two mutually exclusive projects:
What is the IRR for each of these projects? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Using the IRR decision rule, which project should the company accept?
If the required return is 11 percent, what is the NPV for each of these projects? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
At what discount rate would the company be indifferent between these two projects? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
%
Year Cash Flow (A) Cash Flow (B) 0 –$ 29,600 –$ 29,600 1 15,000 4,600 2 12,900 10,100 3 9,500 15,800 4 5,400 17,400Explanation / Answer
Answer (a-1)
IRR
Project A
19.92%
Project B
18.20%
Answer (a-2)
Using IRR decision, Project A should be accepted
Answer (a-3)
Is this decision necessarily correct - No
Answer (b-1)
NPV
Project A
$ 4886.91
Project B
$ 5756.27
Answer (b-2)
Company chooses Project B if it applied NPV rule
Answer (c)
Discount rate = 14.33%
Year
0
1
2
3
4
Project A
-29600
15000
12900
9500
5400
Project B
-29600
4600
10100
15800
17400
Calculation of IRR
Project A
Let r be the rate of return at which NPV = 0, that is
-29600 + 15000/(1+r) + 12900/(1+r)^2 + 9500/(1+r)^3 + 5400/(1+r)^4 = 0
Let r = 20%, LHS will be
= -29600 + 15000/(1.20) + 12900/(1.20)^2 + 9500/(1.20)^3 + 5400/(1.20)^4
= - 29600 + 15000 * 0.833333 + 12900 * 0.694444 + 9500 * 0.578704 + 5400 *0.482253
= -29600 + 12500 + 8958.333 + 5497.685 + 2604.167
= -39.8148
Let r = 19%, LHS will be
= -29600 + 15000/(1.19) + 12900/(1.19)^2 + 9500/(1.19)^3 + 5400/(1.19)^4
= - 29600 + 15000 * 0.840336 + 12900 * 0.706165 + 9500 * 0.593416 + 5400 * 0.498669
= -29600+12605..04+9109.526+5637.45+2692.811
= 444.8297
r = 0.19 + (444.8297 * (0.19-0.20))/(-39.8148-444.8297)
r = 0.19 + (4.448297/484.6445)
r = 0.19 + 0.00917847 = 0.19917847 or 19.92% (rounded off)
Project B
Let r be the rate of return which makes NPV = 0, then
-29600 + 4600/(1+r) + 10100/(1+r)^2 + 15800/(1+r)^3 + 17400/(1+r)^4 = 0
Let r = 18%, LHS will be
= -29600 + 4600/(1.18) + 10100/(1.18)^2 + 15800/(1.18)^3 + 17400/(1.18)^4
= -29600 + 4600 * 0.847458 + 10100 * 0.718184 + 15800 * 0.608631 + 17400 * 0.515789
= -29600 + 3898.305 + 7253.663 + 9616.368 + 8974.726
= 143.062
Let r = 18.5%
= -29600 + 4600/(1.185) + 10100/(1.185)^2 + 15800/(1.185)^3 + 17400/(1.185)^4
= -29600 + 4600 * 0.843882 + 10100 * 0.712137 + 15800 * 0.600959 + 17400 * 0.507139
= -29600 + 3881.857 + 7192.58 + 9495.155 + 8824.21
= -206.199
r= 0.18 + (143.062 * (0.18-0.0185))/(-206.199-143.062)
r = 0.18 + (0.71531/349.261)
r = 0.18 + 0.002048 = 0.182048 or 18.20% (rounded off)
Calculation of NPV
Required rate of return = 11%
Project A
NPV = -29600 + 15000/(1.11) + 12900/(1.11)^2 + 9500/(1.11)^3 + 5400/(1.11)^4
NPV = -29600 + 15000 * 0.900901 + 12900 * 0.811622 + 9500 * 0.731191 + 5400 * 0.658731
NPV = -29600 + 13513.51 + 10469.93 + 6946.318 + 3557.147
NPV = 4886.908 or 4886.91 (rounded off)
Project B
NPV = -29600 + 4600/(1.11) + 10100/(1.11)^2 + 15800/(1.11)^3 + 17400/(1.11)^4
NPV = -29600 + 4600 * 0.900901 + 10100 * 0.811622 + 15800 * 0.731191 + 17400 * 0.658731
NPV = -29600 + 4144.144 + 8197.387 + 11552.82 + 11461.92
NPV = 5756.273 or 5756.27 (rounded off)
Let r be the discount rate at which the company will be indifferent to two projects. That is
-29600 + 15000/(1+r) + 12900/(1+r)^2 + 9500/(1+r)^3 + 5400/(1+r)^4 = -29600 + 4600/(1+r) + 10100/(1+r)^2 + 15800/(1+r)^3 + 17400/(1+r)^4
-29600 + 15000/(1+r) + 12900/(1+r)^2 + 9500/(1+r)^3 + 5400/(1+r)^4 – (-29600 + 4600/(1+r) + 10100/(1+r)^2 + 15800/(1+r)^3 + 17400/(1+r)^4) = 0
-29600 + 15000/(1+r) + 12900/(1+r)^2 + 9500/(1+r)^3 + 5400/(1+r)^4 + 29600 - 4600/(1+r) - 10100/(1+r)^2 - 15800/(1+r)^3 - 17400/(1+r)^4 = 0
(15000 – 4600)/(1+r) + (12900 – 10100)/(1+r)^2 + (9500-15800)/(1+r)^3 + (5400-17400)/(1+r)^4 =0
10400/(1+r) + 2800/(1+r)^2 – 6300/(1+r)^3 – 12000/(1+r)^4 = 0
Let r = 14%, LHS will be
= 10400/(1.14) + 2800/(1.14)^2 – 6300/(1.14)^3 – 12000/(1.14)^4
= 10400 * 0.877193 + 2800 * 0.769468 – 6300 * 0.674972 – 12000 * 0.59208
= 9122.807 + 2154.509 – 4252.32 – 7104.96
= -79.9678
Let r = 14.5%, LHS will be
= 10400/(1.145) + 2800/(1.145)^2 – 6300/(1.145)^3 – 12000/(1.145)^4
= 10400 * 0.873362 + 2800 * 0.762762 – 6300 * 0.666168 – 12000 * 0.581806
= 9082.969 + 2135.733 – 4196.86 – 6981.67
= 40.17701
r = 0.14 + (-79.9678 * (0.14-0.145))/(40.17701-(-79.9678))
r = 0.14 + (0.399839 / 120.14481)
r = 0.14 +0.00332797
r = 0.143327 or 14.33% (rounded off)
IRR
Project A
19.92%
Project B
18.20%
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