Chapter 16, Problem 16.31P

To determine

Concept Introduction:

Time value of money: Time value of money is the concept that differentiates the value of money received today and the value of same money received in future. According to this concept, the same amount of money to be received in future shall have lower present value (value of the money today) due to the interest that could be earned on that money.

NPV: Net present value (NPV) is the method to evaluate the project feasibility. This method calculates the present value of cash inflows and outflows, and then calculates the net present value of the investment. A project should be accepted if it has a positive NPV. The formula to calculate the NPV is as follows:

  $NPV= Presentvalueofcashinflows–Presentvalueofcashoutflows$

IRR: Internal Rate of Return (IRR) is the rate at which the NPV of the project is 0 or we can say that IRR is the rate of return at which the project is at breakeven. IRR is calculated using excel or approximation method.

Payback Period: Payback period is the period in which the project recovers its initial cost of the investment. It can be calculated by dividing the initial investment by the annual cash inflow from the project. The formula to calculate the Payback period is as follows:

  $PaybackPeriod=\frac{InitialInvestment}{AnnualCash\inf low}$

Requirement-a:

To Calculate:

The Net present value of the investment

Answer to Problem 16.31P

The Net present value of the investment is $ (10,361.88)

Explanation of Solution

The Net present value of the investment is calculated as follows;

Year	Cash flows	PVF (10%)	PV
	A	B	=A*B
0	$ (280,000.00)	1.0000	$ (280,000.00)
1	$ 42,000.00	0.9091	$ 38,181.82
2	$ 42,000.00	0.8264	$ 34,710.74
3	$ 42,000.00	0.7513	$ 31,555.22
4	$ 42,000.00	0.6830	$ 28,686.57
5	$ 42,000.00	0.6209	$ 26,078.70
6	$ 42,000.00	0.5645	$ 23,707.91
7	$ 42,000.00	0.5132	$ 21,552.64
8	$ 42,000.00	0.4665	$ 19,593.31
9	$ 42,000.00	0.4241	$ 17,812.10
10	$ 72,000.00	0.3855	$ 27,759.12
	(42000+30000)
NPV			$ (10,361.88)

To determine

Concept Introduction:

Time value of money: Time value of money is the concept that differentiates the value of money received today and the value of same money received in future. According to this concept, the same amount of money to be received in future shall have lower present value (value of the money today) due to the interest that could be earned on that money.

NPV: Net present value (NPV) is the method to evaluate the project feasibility. This method calculates the present value of cash inflows and outflows, and then calculates the net present value of the investment. A project should be accepted if it has a positive NPV. The formula to calculate the NPV is as follows:

  $NPV= Presentvalueofcashinflows–Presentvalueofcashoutflows$

IRR: Internal Rate of Return (IRR) is the rate at which the NPV of the project is 0 or we can say that IRR is the rate of return at which the project is at breakeven. IRR is calculated using excel or approximation method.

Payback Period: Payback period is the period in which the project recovers its initial cost of the investment. It can be calculated by dividing the initial investment by the annual cash inflow from the project. The formula to calculate the Payback period is as follows:

  $PaybackPeriod=\frac{InitialInvestment}{AnnualCash\inf low}$

Requirement-b:

To Calculate:

The Present value ratio to investment

Answer to Problem 16.31P

The Present value ratio to investment is
-3.70%

Explanation of Solution

The Present value ratio to investment is calculated as follows:

Year	Cash flows	PVF (10%)	PV
	A	B	=A*B
0	$ (280,000.00)	1.0000	$ (280,000.00)
1	$ 42,000.00	0.9091	$ 38,181.82
2	$ 42,000.00	0.8264	$ 34,710.74
3	$ 42,000.00	0.7513	$ 31,555.22
4	$ 42,000.00	0.6830	$ 28,686.57
5	$ 42,000.00	0.6209	$ 26,078.70
6	$ 42,000.00	0.5645	$ 23,707.91
7	$ 42,000.00	0.5132	$ 21,552.64
8	$ 42,000.00	0.4665	$ 19,593.31
9	$ 42,000.00	0.4241	$ 17,812.10
10	$ 72,000.00	0.3855	$ 27,759.12
	(42000+30000)
NPV			$ (10,361.88)
Investment			$ 280,000.00
Present value to Investment			-3.70%

To determine

Concept Introduction:

Time value of money: Time value of money is the concept that differentiates the value of money received today and the value of same money received in future. According to this concept, the same amount of money to be received in future shall have lower present value (value of the money today) due to the interest that could be earned on that money.

NPV: Net present value (NPV) is the method to evaluate the project feasibility. This method calculates the present value of cash inflows and outflows, and then calculates the net present value of the investment. A project should be accepted if it has a positive NPV. The formula to calculate the NPV is as follows:

  $NPV= Presentvalueofcashinflows–Presentvalueofcashoutflows$

IRR: Internal Rate of Return (IRR) is the rate at which the NPV of the project is 0 or we can say that IRR is the rate of return at which the project is at breakeven. IRR is calculated using excel or approximation method.

Payback Period: Payback period is the period in which the project recovers its initial cost of the investment. It can be calculated by dividing the initial investment by the annual cash inflow from the project. The formula to calculate the Payback period is as follows:

  $PaybackPeriod=\frac{InitialInvestment}{AnnualCash\inf low}$

Requirement-c:

To Calculate:

The Internal Rate of Return

Answer to Problem 16.31P

The Internal Rate of Return is 9.17%

Explanation of Solution

The Internal Rate of Return is calculated as follows:

Year	Cash flows
	A
0	$ (280,000.00)
1	$ 42,000.00
2	$ 42,000.00
3	$ 42,000.00
4	$ 42,000.00
5	$ 42,000.00
6	$ 42,000.00
7	$ 42,000.00
8	$ 42,000.00
9	$ 42,000.00
10	$ 72,000.00
	(42000+30000)
IRR	9.17%
(Using the excel IRR formula)

To determine

Concept Introduction:

Time value of money: Time value of money is the concept that differentiates the value of money received today and the value of same money received in future. According to this concept, the same amount of money to be received in future shall have lower present value (value of the money today) due to the interest that could be earned on that money.

NPV: Net present value (NPV) is the method to evaluate the project feasibility. This method calculates the present value of cash inflows and outflows, and then calculates the net present value of the investment. A project should be accepted if it has a positive NPV. The formula to calculate the NPV is as follows:

  $NPV= Presentvalueofcashinflows–Presentvalueofcashoutflows$

IRR: Internal Rate of Return (IRR) is the rate at which the NPV of the project is 0 or we can say that IRR is the rate of return at which the project is at breakeven. IRR is calculated using excel or approximation method.

Payback Period: Payback period is the period in which the project recovers its initial cost of the investment. It can be calculated by dividing the initial investment by the annual cash inflow from the project. The formula to calculate the Payback period is as follows:

  $PaybackPeriod=\frac{InitialInvestment}{AnnualCash\inf low}$

Requirement-d:

To Calculate:

The Payback period of the project

Answer to Problem 16.31P

The Payback period of the project is 6.67 years

Explanation of Solution

The Payback period of the project is calculated as follows:

Investment (A)	$ 280,000
Annual Cash flows (B)	$ 42,000
Payback period (Years) (A/B)	6.67