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13. Relationships: Discounted Techniques
Fill in the blanks for each of the following independent cases. In all cases, the investment has a useful life of ten (10) years and no salvage value. Round off factors to three decimal places.
Project Annual Cash Flow
1
P 45,000
234
P 75,000 (E) 62,073
Investment P 188,640 (C) 3220
P 300,000
(G) 200
P 450,000
Cost of Capital 14%
12%
IRR (A) 20 18%
(F)(0%
16%
NPV (B) 7080 (D) £6.700 P 81,440
12%
(H) 18%
P 115,000

 

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To determine the missing values, let's analyze each case:

Case A:

• The IRR is 20%.
• The cost of capital is 14%.

Case B:
- The NPV is £6,700.

Case C:

• The investment is P 188,640.
• The cost of capital is 12%.

Case D:
- The NPV is P 81,440.

Case E:

• The annual cash flow is P 75,000.
• The NPV is P 62,073.

Case F:

• The IRR is 0%.
• The cost of capital is 16%.

Case G:

• The investment is P 300,000.
• The IRR is 18%.

Case H:

• The cost of capital is 18%.
• The investment is P 115,000.

Now, let's calculate the missing values.

Case A:
To find the NPV, we can use the formula NPV = (Annual Cash Flow / (1 + cost of capital)^n) - Investment, where n is the number of years (10).

NPV = (45,000 / (1 + 0.14)^10) - Investment
7080 = (45,000 / (1.14)^10) - Investment

Solving for Investment, we find:
Investment = 45,000 / (1.14)^10 - 7080
Investment = 45,000 / 2.812 - 7080
Investment = 15,997.16 - 7080
Investment = 9,917.16

Therefore, the missing value in Case A is Investment = P 9,917.16.

Case B:
The missing value is the NPV, which is already given as £6,700.

Case C:
The missing value is the cost of capital.

To find the cost of capital, we can rearrange the NPV formula as follows:
NPV = (Annual Cash Flow / (1 + cost of capital)^n) - Investment

Rearranging the formula:
cost of capital = (Annual Cash Flow / NPV)^(1/n) - 1
cost of capital = (3220 / 188,640)^(1/10) - 1
cost of capital = 0.017 - 1
cost of capital = 0.017

Therefore, the missing value in Case C is the cost of capital = 1.7%.

Case D:
The missing value is the NPV, which is already given as P 81,440.

Case E:
The missing value is the annual cash flow.

To find the annual cash flow, we can rearrange the NPV formula as follows:
NPV = (Annual Cash Flow / (1 + cost of capital)^n) - Investment

Rearranging the formula:
Annual Cash Flow = (NPV + Investment) * (1 + cost of capital)^n
Annual Cash Flow = (62,073 + 188,640) * (1 + 0.12)^10
Annual Cash Flow = 250,713 * 2.208
Annual Cash Flow = P 553,111.34

Therefore, the missing value in Case E is the annual cash flow = P 553,111.34.

Case F:
To find the NPV, we can use the formula NPV = (Annual Cash Flow / (1 + cost of capital)^n) - Investment, where n is the number of years (10).

NPV = (75,000 / (1 + 0.16)^10) - Investment
0 = (75,000 / (1.16)^10) - Investment

Solving for Investment, we find:
Investment = 75,000 / (1.16)^10
Investment = 75,000 / 3.172
Investment = 23,645.14

Therefore, the missing value in Case F is Investment = P 23,645.14.

Case G:
The missing value is the investment, which is already given as P 300,000.

Case H:
The missing value is the cost of capital.

The cost of capital is given as 18%, so there is no missing value in Case H.

In summary, the missing values are:
A) Investment = P 9,917.16
B) NPV = £6,700
C) Cost of Capital = 1.7%
D) NPV = P 81,440
E) Annual Cash Flow = P 553,111.34
F) Investment = P 23,645.14
G) Investment = P 300,000
H) No missing value