Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors. There are many capital budgeting techniques. The two techniques that will be discussed here is – 1. Payback period of the investment 2. Net present value of the investment 1. Payback period – Payback period of the investment is calculated as under – P a y b a c k p e r i o d = I n i t i a l I n v e s t m e n t A n n u a l n e t c a s h i n f l o w This is how we calculate payback period in case of even annual net cash inflows. 2. Net present value – The net present value is calculated as under – N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s − I n i t i a l I n v e s t m e n t Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) – T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s X P r e s e n t v a l u e o f A n n u i t y ( P V A F ) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s This is how we calculate net present value of an investment. Requirement 1 To compute: Payback period of Investment

Question

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Answer 1

Question

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Conclusion

Thus, the payback period of the investment = 5 years.

To determine

Requirement 2

To compute:

Net present value of the investment.

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note – The following PVAF table has been used for referring PVAF @ 8 % for 8 years.

Loose Leaf for Fundamental Accounting Principles, Chapter 25, Problem 29QS

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Answer 2

Question

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Conclusion

Thus, the payback period of the investment = 5 years.

To determine

Requirement 2

To compute:

Net present value of the investment.

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note – The following PVAF table has been used for referring PVAF @ 8 % for 8 years.

Loose Leaf for Fundamental Accounting Principles, Chapter 25, Problem 29QS

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Answer 3

Question

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Conclusion

Thus, the payback period of the investment = 5 years.

To determine

Requirement 2

To compute:

Net present value of the investment.

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note – The following PVAF table has been used for referring PVAF @ 8 % for 8 years.

Loose Leaf for Fundamental Accounting Principles, Chapter 25, Problem 29QS

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Answer 4

Question

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Conclusion

Thus, the payback period of the investment = 5 years.

To determine

Requirement 2

To compute:

Net present value of the investment.

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note – The following PVAF table has been used for referring PVAF @ 8 % for 8 years.

Loose Leaf for Fundamental Accounting Principles, Chapter 25, Problem 29QS

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Answer 5

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Conclusion

Thus, the payback period of the investment = 5 years.

To determine

Requirement 2

To compute:

Net present value of the investment.

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note – The following PVAF table has been used for referring PVAF @ 8 % for 8 years.

Loose Leaf for Fundamental Accounting Principles, Chapter 25, Problem 29QS

Answer 6

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Conclusion

Thus, the payback period of the investment = 5 years.

Answer 7

Chapter 25, Problem 29QS

To determine

Concept Introduction:

Capital budgeting is a planning process used to know whether a long term investment or options like to keep the old machine will be profitable or not involving factors like present value factors.

There are many capital budgeting techniques. The two techniques that will be discussed here is –

1. Payback period of the investment

2. Net present value of the investment

1. Payback period –

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

This is how we calculate payback period in case of even annual net cash inflows.

2. Net present value –

The net present value is calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment can be defined as the cash outlay incurred at the beginning of the product and total present value of cash inflows is computed as under (in case of even cash inflows) –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

This is how we calculate net present value of an investment.

Requirement 1

To compute:

Payback period of Investment

Answer 8

Expert Solution

Answer to Problem 29QS

Solution:

Payback period of Investment = 5 years

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Payback period of the investment is calculated as under –

$P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w}$

Given,

• Initial investment = $ 80 million

• Annual net cash flows = $ 16 million

$\begin{array}{l} P a y b a c k p e r i o d = \frac{I n i t i a l I n v e s t m e n t}{A n n u a l n e t c a s h i n f l o w} \\ P a y b a c k p e r i o d = \frac{$ 80 m i l l i o n}{$ 16 m i l l l i o n} \\ P a y b a c k p e r i o d = 5 y e a r s \end{array}$

Answer 13

Conclusion

Thus, the payback period of the investment = 5 years.

Answer 14

To determine

Requirement 2

To compute:

Net present value of the investment.

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$

Conclusion

Thus, the net present value of the investment = $ 11.952 million.

Note – The following PVAF table has been used for referring PVAF @ 8 % for 8 years.

Loose Leaf for Fundamental Accounting Principles, Chapter 25, Problem 29QS

Answer 15

To determine

Requirement 2

To compute:

Net present value of the investment.

Answer 16

Expert Solution

Answer to Problem 29QS

Solution:

Net present value of the investment = $11.952 million

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Expert Solution

Answer 20

Explanation of Solution

Given,

Initial investment = $ 80 million

Total present value of cash inflows will be calculated as under –

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

Now, for present value of cash inflows –

Given –

• Annual net cash inflow = $ 16 million

• Number of years = 8 years

• Interest rate or required rate = 8%

Total present value of cash inflows =

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = A n n u a l n e t c a s h i n f l o w s \\ X P r e s e n t v a l u e o f A n n u i t y (P V A F) a t a g i v e n r a t e f o r a g i v e n n u m b e r o f y e a r s \end{array}$

$\begin{array}{l} T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 16 m i l l i o n X 5.747 \\ T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s = $ 91.952 m i l l i o n \end{array}$

Net present value of the investment will be calculated as under –

$N e t p r e s e n t v a l u e = T o t a l p r e s e n t v a l u e o f c a s h i n f l o w s - I n i t i a l I n v e s t m e n t$

Initial investment = $ 80 million

Total present value of cash inflows = $ 91.952 million

$\begin{array}{l} N e t p r e s e n t v a l u e = $ 91 .952 million - $ 80 million \\ N e t p r e s e n t v a l u e = $ 11.952 m i l l i o n \end{array}$