For the following two projects, determine the Payback Period Discounted Payback Net Present Value Profitability Index...

For the following two projects, determine the

Payback Period
Discounted Payback
Net Present Value
Profitability Index (Benefit-Cost Ratio)
Internal Rate of Return
Modified Internal Rate of Return

	Project A			Project B
Year		Net Income	Cash Flow		Net Income	Cash Flow
0			(15,000)			(19,000)
1		5,000	6,000		3,000	4,000
2		5,000	6,000		5,000	6,000
3		5000	6,000		7,000	8,000
4		5,000	6,000		11,000	12,000
Risk Index	1.80			.60

The firm’s cost of capital k_o is 15% and the risk free rate R_f is 10%. The firm assesses risk and assigns a risk index to determine a risk adjusted discount rate. An index of 1.0 would be assigned to an average risk project.

To determine risk adjusted rates the firm uses the following equation:

Risk Adjusted Rate (RADR) = R_f + [Risk Index (k_o – R_f)

Task: Rank the projects in accordance with each method of analysis.

Solutions

Expert Solution

Project A :

Year	Cash Flow	Cummulative Cashflow	Discounting factor = 1/ ( 1+ r)^n	Present value	Cummulative present value
1	6000	6000	0.840336134	5042.016807	5042.016807
2	6000	12000	0.706164819	4236.988913	9279.00572
3	6000	18000	0.593415814	3560.494885	12839.5006
4	6000	24000	0.498668751	2992.012508	15831.51311
			Total	15831.51311

Risk adjusted rated for Project A = 10 + 1.8* ( 15 - 10) = 19%

Payback period = 2 + ( 15000-12000) / 6000 = 2.5 years

Discounted payback period = 3 + ( 15000 - 12839) / 2992.01 = 3.72 years

Net present value = present value of cash inflows - initial investment = 15831.51 - 15000 = 831.51

Profitability index = Present value of cash inflows / initial invetsmnet = 15831.51 / 15000 = 1.055

Project B :

Year	Cash Flow	Cummulative Cashflow	Discounting factor = 1/ ( 1+ r)^n	Present value	Cummulative present value
1	4000	4000	0.884955752	3539.823009	3539.823009
2	6000	10000	0.783146683	4698.8801	8238.703109
3	8000	18000	0.693050162	5544.401298	13783.10441
4	12000	30000	0.613318728	7359.824732	21142.92914
			Total	21142.92914

Payback period = 3 + ( 19000 - 18000) / 12000 = 3.08 years

Discounted payback period = 3 + ( 19000 - 13783) / 7359.82 = 3.71 years

Net present value = 21142.93 - 19000 = 2142.93

PI = 21142.93 / 19000 = 1.113

jeff jeffy answered 1 year ago

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