Question

Suppose that you investigate the case of two mutual exclusive investments, investment A and investment B, the annual Net Cash Flows of which are given below: to ti tz tz A (10,000) 4,000 4,000 10,000 B (50,000) 15,000 15,000 40,000 The risk free interest rate is equal to 2% while the market portfolio yields 7% on an annual basis. 4.1 Suppose that these investments refer to a firm the systematic risk factor of which (i.e. beta coefficient) is equal to 0.5. Which investment would you choose according to the Net Present Value (NPV) and the Internal Rate of Return (IRR) investment appraisal techniques? Is there any difference in the decisions made, based on the NPV and the IRR criteria? Why? [15%] 4.2 Suppose that after a careful consideration of the firm under investigation you revise your expectation about the systematic risk factor from 0.5 to 2.4. (i.e. beta coefficient is equal to 2.4). Which investment would you choose according to the NPV and the IRR investment appraisal techniques? Is there any difference in the decisions made, based on the NPV and the IRR criteria? Why? [15%] 4.3. Please explain in detail the role of the beta coefficient in your investment decisions of the previous sub-questions. [20%] Please explain your answers analytically.

Answer 1

Part 4.1) We first need to find the discount rate if the beta is 0.5

Return = risk free rate + beta x (Market return - risk free rate)

Return = 2+ 0.5 x (7- 2)

Now using this as discount rate we need to find out the NPV of both the projects:

Project A

Year	CF	Discount Factor		Discounted CF
0	$ -10,000.00	1/(1+0.045)^0=	1	1*-10000=	$   -10,000.00
1	$      4,000.00	1/(1+0.045)^1=	0.956937799	0.956937799043062*4000=	$       3,827.75
2	$      4,000.00	1/(1+0.045)^2=	0.915729951	0.91572995123738*4000=	$       3,662.92
3	$    10,000.00	1/(1+0.045)^3=	0.876296604	0.876296604054909*10000=	$       8,762.97
				NPV = Sum of all Discounted CF	$       6,253.64

Project B

Year	CF	Discount Factor		Discounted CF
0	$ -50,000.00	1/(1+0.045)^0=	1	1*-50000=	$   -50,000.00
1	$    15,000.00	1/(1+0.045)^1=	0.956937799	0.956937799043062*15000=	$    14,354.07
2	$    15,000.00	1/(1+0.045)^2=	0.915729951	0.91572995123738*15000=	$    13,735.95
3	$    40,000.00	1/(1+0.045)^3=	0.876296604	0.876296604054909*40000=	$    35,051.86
				NPV = Sum of all Discounted CF	$    13,141.88

According to NPV rule the project with higher NPV should be selected, which is project B

IRR is the rate for which the NPV = 0, , to find it, we need to use a financial calculator or Excel's goal seek function:

Project A: IRR comes to 29.97%

Year	CF	Discount Factor		Discounted CF
0	$ -10,000.00	1/(1+0.299724444528588)^0=	1	1*-10000=	$   -10,000.00
1	$      4,000.00	1/(1+0.299724444528588)^1=	0.769393854	0.769393854374033*4000=	$       3,077.58
2	$      4,000.00	1/(1+0.299724444528588)^2=	0.591966903	0.591966903148531*4000=	$       2,367.87
3	$    10,000.00	1/(1+0.299724444528588)^3=	0.455455697	0.455455697275308*10000=	$       4,554.56
				NPV = Sum of all Discounted CF	$               0.00

Project B: IRR = 15.69%

Year	CF	Discount Factor		Discounted CF
0	$ -50,000.00	1/(1+0.156959551013122)^0=	1	1*-50000=	$   -50,000.00
1	$    15,000.00	1/(1+0.156959551013122)^1=	0.864334452	0.864334452422579*15000=	$    12,965.02
2	$    15,000.00	1/(1+0.156959551013122)^2=	0.747074046	0.74707404564464*15000=	$    11,206.11
3	$    40,000.00	1/(1+0.156959551013122)^3=	0.645721836	0.645721836161381*40000=	$    25,828.87
				NPV = Sum of all Discounted CF	$               0.00

IRR rule states that the project with higher IRR should be selected which is project A however in case of conflicts of the 2 rules, NPV rule reigns supreme, so project B should be selected.

.

Part 4.2) We first need to find the discount rate if the beta is 2.4

Return = risk free rate + beta x (Market return - risk free rate)

Return = 2+ 2.4 x (7- 2)

Return - 17%

Now using this as discount rate we need to find out the NPV of both the projects:

Project A

Year	CF	Discount Factor		Discounted CF
0	$ -10,000.00	1/(1+0.17)^0=	1	1*-10000=	$   -10,000.00
1	$      4,000.00	1/(1+0.17)^1=	0.854700855	0.854700854700855*4000=	$       3,418.80
2	$      4,000.00	1/(1+0.17)^2=	0.730513551	0.730513551026372*4000=	$       2,922.05
3	$    10,000.00	1/(1+0.17)^3=	0.624370556	0.624370556432796*10000=	$       6,243.71
				NPV = Sum of all Discounted CF	$ 2,584.56

Project B

Year	CF	Discount Factor		Discounted CF
0	$ -50,000.00	1/(1+0.17)^0=	1	1*-50000=	$   -50,000.00
1	$    15,000.00	1/(1+0.17)^1=	0.854700855	0.854700854700855*15000=	$    12,820.51
2	$    15,000.00	1/(1+0.17)^2=	0.730513551	0.730513551026372*15000=	$    10,957.70
3	$    40,000.00	1/(1+0.17)^3=	0.624370556	0.624370556432796*40000=	$    24,974.82
				NPV = Sum of all Discounted CF	$ -1,246.96

According to NPV rule the project with higher NPV should be selected, which is project A

IRR remains the same as in previous question

IRR rule states that the project with higher IRR should be selected which is project A

Part 4.3) Beta has a multiplier effect on the rate of return calculation which changes the discount rate and thus changes the NPV calculation. As project B has an IRR of 15.69% and Project A of 29.97%, after 15.69% to 29.97%, project A will still have a positive NPV while project B will have a negative NPV. So project A will become desirable between discount rates of 15.69 and 29.97 while before 15.69, project B will be desirable