RAK Corp. is evaluating a project with the following cash flows: Year Cash Flow
ID: 2778804 • Letter: R
Question
RAK Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 –$ 30,000 1 12,200 2 14,900 3 16,800 4 13,900 5 – 10,400 The company uses an interest rate of 8 percent on all of its projects. Calculate the MIRR of the project using the discounting approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) MIRR % Calculate the MIRR of the project using the reinvestment approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) MIRR % Calculate the MIRR of the project using the combination approach. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) MIRR %
Explanation / Answer
MIRR of the project using Discounting Approach = 19.81%
MIRR of the project using investment method = 14.86%
MIRR of the project using combined method =13.54%
Discount rate = 8%
MIRR Discounting Approach
Year
Cash Flow
Adjusted value
Modified CF (CF+Adj)
0
-30,000
-10400/1.08^5 = -10400/1.4693280768
= -7078.065
-37,078.065
1
12,200
12,200
2
14,900
14,900
3
16,800
16,800
4
13,900
13,900
5
-10,400
0
Let r be the MIRR which makes the total values of above flows equal to zero
-37,078.065 +12,200/(1+r) + 14,900/(1+r)^2 + 16,800/(1+r)^3 + 13,900/(1+r)^4 = 0
If r = 20%,then LHS of the equation will be
--37,078.065 +12,200/1.20 + 14,900/(1.2)^2 + 16,800/(1.2)^3 + 13,900/(1.2)^4
= --37,078.065 +12,200/1.20 + 14,900/1.44 + 16,800/1.728 + 13,900/2.0736
= -37078.065 + 10166.667 + 10347.222 + 9722.22 + 6703.317
= -138.639
If r = 19%, then LHS of the equal will be
--37,078.065 +12,200/1.19 + 14,900/(1.19)^2 + 16,800/(1.19)^3 + 13,900/(1.19)^4
= --37,078.065 +12,200/1.19 + 14,900/1.4161 + 16,800/1.685159 + 13,900/2.00533921
=-37078.065 +10252.101 +10521.856 +9969.386+6931.496
= 596.774
MIRR = 0.19 + {[(596.774)*(0.19 – 0.20)]/(-138.639-596.774)}
= 0.19 + { (596.774 * -0.01)/(-735.413)}
= 0.19 + (5.96774/735.413)
= 0.19 + 0.0081148
= 0.1981148 or 19.81% (rounded off)
Calculation of investment method
Year
Cash Flow
Compounding factor
Adjusted value
Modified CF (CF+Adj)
0
-30,000
-30,000
1
12,200
1.08^4 = 1.36048896
0
2
14,900
1.08^3 = 1.259712
0
3
16,800
1.08^2 = 1.1664
0
4
13,900
1.08
0
5
-10,400
16597.965+ 18769.709+19595.52
+15012 = 69975.194
59975.194
For calculating adjusted value in investment method positive cash flows are multiplied by the future value factor at 8% to take it to the project end. That is the first flow is multiplied by fv factor FV (8,4) or 1.08^4 second one with FV(8,3) and so on. The sum is added to the project end
12200 * 1.08^4 + 14900 * 1.08^3 + 16800 * 1.08^2 + 13900 * 1.08
Let r is the MIRR which makes the modified cash flows equals zero. That is
-30,000 + 59975.194/(1+r)^5 = 0
59975.194/(1+r)^5 = 30000
(1+r)^5 =59975.194/30000
(1+r)^5 = 1.999173
1+r = (1.999173)^1/5 = 1.148603
r = 1.148603 – 1 = 0.148603 or 14.86%
Calculation using combined method
Year
Cash Flow
Adjusted value
Modified CF (CF+Adj)
0
-30,000
-10400/1.08^5 = -10400/1.4693280768
= -7078.065
-37,078.065
1
12,200
0
2
14,900
0
3
16,800
0
4
13,900
0
5
-10,400
16597.965+ 18769.709+19595.52
+15012 = 69975.194
69975.194
Let r be IRR of the project which makes the modified cash flows equals zero
-37078.065 + 69975.194/(1+r)^5 = 0
69975.194/(1+r)^5 = 37078.065
(1+r)^5 = 69975.194/37078.065
1+r = (1.8872396)^1/5
= 1.135443
r = 1.135443 – 1 = 0.135443 or 13.54%
Year
Cash Flow
Adjusted value
Modified CF (CF+Adj)
0
-30,000
-10400/1.08^5 = -10400/1.4693280768
= -7078.065
-37,078.065
1
12,200
12,200
2
14,900
14,900
3
16,800
16,800
4
13,900
13,900
5
-10,400
0
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