Question

Investment Decision Rules

Problem 1

Coral, Inc. is evaluating investment opportunities and should decide between two mutually exclusive projects: B or C. Both projects require the same initial investments 18 million and generate different cash flows as follow:

• Project (B) generates 2.2 million in perpetuity growing at 3.0% (forever)
• Project (C) generate 1.6 million in perpetuity growing at 4.0% ((forever)

1. If Coral is using the IRR to make her final decision, calculate the IRR of each of the following project.
2. Calculate the NPV of both project if the required rate is 10%
3. Calculate the crossover rate (If  existing)
4. Graph the NPV function of both project and discuss (You can use excel and then insert your Graph here)

Answer 1

IRR is the rate at which present value of perpetual cashflows equal the investment made at the start.

Part a

IRR of Project B

Initial investments (in Mn)	18
Perpetual cashflows (in Mn)	2.2
Constant growth rate	3%

Present value of perpetual cashflows = Cashflows / (discount rate % - growth %)

Lets take IRR of Project B to be a%; Therefore at IRR of a% present value of perpetual cashflows equal the initial investment

Initial investment = Present value of cashflows

Initial investment = Cashflows / (discount rate% - growth %)

Initial investment = Cashflows / (IRR% - growth %)

Initial investment = Cashflows / (IRR% - growth %)

18 = 2.2 / (a% - 3%)

(a% - 3%) = 2.2 /18

(a% - 3%) = 2.2 /18

(a% - 3%) = 0.1222

a% = 0.1222 + 0.03

a% = 0.1222 + 0.03

Therefore IRR is 15.22%

IRR of Project B

Initial investments (in Mn)	18
Perpetual cashflows (in Mn)	1.6
Constant growth rate	4%

Present value of perpetual cashflows = Cashflows / (discount rate % - growth %)

Lets take IRR of Project B to be b%; Therefore at IRR of a% present value of perpetual cashflows equal the initial investment

Initial investment = Present value of cashflows

Initial investment = Cashflows / (discount rate% - growth %)

Initial investment = Cashflows / (IRR% - growth %)

Initial investment = Cashflows / (IRR% - growth %)

18 = 1.6 / (b% - 4%)

(b% - 4%) = 1.6 /18

(b% - 4%) = 1.6 /18

(b% - 4%) = 0.0889

b% = 0.0889 + 0.04

b% = 0.0889 + 0.04

Therefore IRR is 12.89%

Part b : NPV computation

Project B

Present value of cashflows @ 10% discount rate

Cashflows	2.2
Discount rate	10%
Growth rate	3%
Present value of cashflows	Cashflows / (Discount rate - growth rate)
Present value of cashflows	2.2 / (10%-3%)
Present value of cashflows	2.2 / (10%-3%)
Present value of cashflows	31.43
Initial investment	18
NPV (Present value of cashflows - initial investment)	13.43

Project C

Present value of cashflows @ 10% discount rate

Cashflows	1.6
Discount rate	10%
Growth rate	4%
Present value of cashflows	Cashflows / (Discount rate - growth rate)
Present value of cashflows	1.6 / (10%-4%)
Present value of cashflows	1.6 / (10%-4%)
Present value of cashflows	26.67
Initial investment	18
NPV (Present value of cashflows - initial investment)	8.67

Crossover rate

Crossover rate is the discount rate at which NPV of both projects are equal. Lets assume crossover rate to be x%

NPV of B = NPV of C

2.2 / (x%-3%) - 18 = 1.6 / (x%-4%) -18

2.2 / (x%-3%) = 1.6 / (x%-4%)

2.2 / (x%-3%) = 1.6 / (x%-4%)

1.6 * (x%-3%) = 2.2*(x%-4%)

1.6x%-4.8% = 2.2x%-68.8%

8.8%-4.8% = 2.2x%-1.6x%

4% = 0.6x%

x = 6.67%; therefore crossove rate is 6.67%

NPV Table

Project B	13.43
Project C	8.67

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