**QUESTION 1**

*Explain what is meant by the time value of money and why a bird in the hand is worth two or more in the bush. Which capital budgeting approach(es) ignores this concept?*

The time value of money is certainly not a new concept. The definition of the time value of money indicates that “money received sooner rather later allows one to use the funds for investment or consumption purposes”. the value money at the present time is worth more than the same amount in the future due to its potential earning capacity, $1 today is worth more than $1 in the future because reasons:

_Inflation makes decline in the purchasing power of money

_Risk in the economic activities

_Money at the present can make interest by itself but money in the future still only the same value. We can put money to work earning more money for us ( earning interest, invested in stocks, real estate or other assets that can appreciate in value)

The fact shows that the monetary has a time value and the interest rate is a measure of time value of money.

For example, if we were given $100 today and invested it at an annual rate of 1%, it could be worth $101 at the end of one year, which is more than you’d have if you received $100 at that point.

We can look at the sentence “a bird in the hand is worth two or more in the bush” to understand the time value of money. A bird in the hand is the money that we hold today, birds in the bush is the cash we will receive from our investment in the future. We can earn interest on money received today, it is better to receive money earlier rather than later.

Payback period is part of capital budgeting approach which ignores the concept of time value of money.

*Why cannot the accounting rate of return be used as a reliable capital budgeting technique? What are its advantages?*

The accounting rate of return is a way of comparing the profits you expect to make from an investment to the amount you need to invest.

The accounting rate of return cannot be used as a reliable capital budgeting technique because this computation attempts to calculate the average book value of an investment by simply averaging the initial and liquidation values.

There are some advantages of the accounting rate of return.

_ It is familiarity, ease of understanding and communication

_ Managers’ performances are often judged using ARR and therefore wish to select projects on the same basis

## QUESTION 2

a. Formula for Cost of Capital

## ➔ Cost of Capital = W_{d} * K_{d} + W_{cs} * k_{cs}

Note: – W_{d} is percentage of debt

- W
_{cs}is percentage of internal common stock

- K
_{d}is after-tax cost of debt

- k
_{cs}is the cost of internal common stock

## ➔ k_{cs} = k_{rf} + β * (k_{m} – k_{rf}) (k_{rf} is risk free rate, k_{m} – k_{rf} is market risk premium, β is systematic risk of stock)

= 0.1 + 0.80 * 0.15

= 0.22

## ➔ K_{d} = k_{d} * (1 – T_{c}) (k_{d} is before-tax cost of debt, T_{c} is tax rate)

Where V_{b} = (V_{b} is bond current market value, I_{t} is interest payment in year t, M is bond maturity)

=111

111 = 11 * (PVIFA_{kd,8}) + 100 * (PVIF_{kd,8})

***Because current market price (111) > par value (100), so k_{d} < coupon rate (interest rate on the debt 11%)

Value | Value | ||

For | k_{d} = 9 | 111.085 | |

k_{d} | 111 | ||

k_{d} = 10 | 105.385 | ||

0.085 | 5.7 |

Note: k_{d} = 0.09 + (0.085/5.7) * 0.01 = 9.01% K_{d} = 9.01 * (1 – 0.3) = 6.31%

Source of Funds | Market Value ($m) | Percentage | |

Debt (par value $100) | 1 | 25% | W_{d} |

Equity | 3 | 75% | Wcs |

Note: Cost of Capital = 0.25 * 6.31 + 0.75 * 0.22 = 1.74

## QUESTION 3

- Follow the content: Require rate of return is 1%

Sale revenue ($) | Expense ($) | Profit ($) | Opportunity cost ($) | |

Cash basis | 50,000 | 40,000 | 10,000 | 0 |

Free credit term | 55,000 | 44,000 | 11,000 | X |

Opportunity cost in free credit term (90days) X = 55,000 * [(1 + 0.01)^{3} – 1] = 1,667 ($)

Actual Gain | |

Cash basis | 10,000 |

Free credit term | 9,333 =(11,000 – 1,667) |

So TLC Ltd will gain less benefit by selling in free credit term compare to selling on cash basis.

- If expenses remain at 80% of sales, the increase in sales is () in order to justify the provision of these credit terms.

Sale revenue ($) | Expense ($) | Profit ($) | Opportunity cost ($) | |

Cash basis | 50,000 | 40,000 | 10,000 | 0 |

Free credit term | 50,000 + | 0.8 * (50,000 + ) | 10,000 + 0.2 | X’ |

X’ = (50,000 +) * [(1 + 0.01)^{3} – 1]

= (50,000 +) * 0.0303

So, in order to increase in sales to justify the provision of free credit term: 10,000 + 0.2 – (50,000 +) * 0.0303 > 10,000

10,000 + 0.2 – 1,500 – 0.0303 > 10,000

> 8,928

## PART B

**QUESTION 1**

The net present value of an investment proposal is equal to the present value of its free cash flow less the investment’s initial outlay. It allows a company to project the projects potential profitability by discounting future cash flow expectations and comparing the sum of these cash flows to the initial capital expenditure required to

fund the project. The net present value can be expressed as :

The economic rationale behind NPV is straightforward. NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account. If a project has a zero NPV, its cash flows are sufficient to repay the dollar cost of the project and provide a return on the dollars invested commensurate with the riskiness of the project. Thus, from an economic perspective, a project with a zero NPV breaks even.

A project with a positive NPV is expected to generate a profit, while a negative NPV signifies that a project is unprofitable.

Calculate the project’s Net Present Value

Operating cash flows = change in earnings before interest and taxes (CEBIT) – change in taxes (CT) + change in depreciation (CD)

Year | Cost Decrease | CT | Initial Investment | % depreciation | CD | EBIT |

1 | 25,000 | 3,200 | 85,000 | 20 | 17,000 | 8,000 |

2 | 25,000 | 880 | 85,000 | 32 | 27,200 | (2,200) |

3 | 25,000 | 3,540 | 85,000 | 19 | 16,150 | (8,850) |

4 | 25,000 | 5,920 | 85,000 | 12 | 10,200 | 14,800 |

5 | 25,000 | 6,260 | 85,000 | 11 | 9,350 | 15,650 |

6 | 25,000 | 7,960 | 85,000 | 6 | 5,100 | 19,900 |

7 | 25,000 | 10,000 | 25,000 |

8 | 25,000 | 10,000 | 25,000 |

Year | Initial Investment and Operating Cash Flows | Present Value Factor at 10% | Present Value |

0 | (85,000) | ||

1 | 21,800 | 0.909 | 19,816 |

2 | 25,880 | 0.826 | 21,376.88 |

3 | 21,460 | 0.751 | 16,116.46 |

4 | 19,080 | 0.683 | 13,031.64 |

5 | 18,740 | 0.621 | 11,637.54 |

6 | 17,040 | 0.564 | 9,610.56 |

7 | 15,000 | 0.513 | 7,695 |

8 | 15,000 | 0.467 | 7,005 |

Total | 106,289.28 |

NPV = = 106,289.28 – 85,000 = 21,289.28

Each customer expects a separate required rate of return, but initial outlay and free cash flow are the same in the firm, thus the NPV is different from each customer.

## QUESTION 2

The Internal Rate of Return (IRR) is the discount rate that generates a zero net present value for a series of future cash flows. This essentially means that IRR is the rate of return that makes the sum of present value of future cash flows and the final market value of a project (or an investment) equal its current market value.

# IO =

The IRR is one of way to make decision acceptation or rejection of project in the business. A capital –budgeting decision criterion that reflects the rate of return a project earns. Mathematically, it is the discount rate that equates the present value of the outflow.

IRR > required rate of return: accept

IRR < required rate of return: reject

# IO =

Where FCFt = the annual free cash flow in time period t (This can take on either positive or negative value)

IO: the initial cash outlay

N: the project‘s expected life.

IRR: the project’s internal rate of return.

# IO =

**Try***i =*16%

Year | Free Cash Flows | PV Factor at 16% | Present Value |

1 | 21,800 | 0.862 | 18,791.6 |

2 | 25,880 | 0.743 | 19,228.84 |

3 | 21,460 | 0.641 | 13,755.86 |

4 | 19,080 | 0.552 | 10,532.16 |

5 | 18,740 | 0.476 | 8,920.24 |

6 | 17,040 | 0.410 | 6,986.4 |

7 | 15,000 | 0.354 | 5,310 |

8 | 15,000 | 0.305 | 4,575 |

Present value of inflows | 88,100.1 | ||

Initial outlay | -85,000 |

**Try***i =*17%

Year | Free Cash Flows | PV Factor at 31% | Present Value |

1 | 21,800 | 0.855 | 18,639 |

2 | 25,880 | 0.731 | 18,918.28 |

3 | 21,460 | 0.624 | 13,391.04 |

4 | 19,080 | 0.534 | 10,188.72 |

5 | 18,740 | 0.456 | 8,545.44 |

6 | 17,040 | 0.390 | 6,645.6 |

7 | 15,000 | 0.333 | 4,995 |

8 | 15,000 | 0.285 | 4,275 |

Present value of inflows | 85,598.08 | ||

Initial outlay | -85,000 |

**Try***i =*18%

Year | Free Cash Flows | PV Factor at 32% | Present Value |

1 | 21,800 | 0.847 | 18,464.6 |

2 | 25,880 | 0.718 | 18,581.84 |

3 | 21,460 | 0.609 | 13,069.14 |

4 | 19,080 | 0.516 | 9,845.28 |

5 | 18,740 | 0.437 | 8,189.38 |

6 | 17,040 | 0.370 | 6,304.8 |

7 | 15,000 | 0.314 | 4,710 |

8 | 15,000 | 0.266 | 3,990 |

Present value of inflows | 83,155.04 | ||

Initial outlay | -85,000 |

## So, IRR = 17%

IRR – internal rate of return is the return which project creates by itself, thus IRR does not depend on customer and it is the same number to them.

## QUESTION 3

*a. What is the project’s payback period?*

The payback period is the number of years needed to recover the initial cash outlay of the capital budgeting project. As this criterion measures how quickly the project will return its original investment, it deals with free cash flows, which measure the true timing of the benefits, rather than accounting profits. Unfortunately, it also ignores the time value of money and does not discount these free cash flows back to the present. The accept-reject criterion centers on whether the project’s payback period is less than or equal to the firm’s maximum desired payback period.

It is calculated using the formula:

Cost of project / Annual cash revenues = Payback period

Year | Initial Investment and Cash Flows |

0 | (85,000) |

1 | 21,800 |

2 | 25,880 |

3 | 21,460 |

4 | 19,080 |

5 | 18,740 |

6 | 17,040 |

7 | 15,000 |

8 | 15,000 |

Cash Flow Year 1 + Cash Flow Year 2 + Cash Flow Year 3 = 21,800 + 25,880 + 21,460 = 69,140

Cash Flow Year 4 = 19,080 Initial Investment = 85,000

So, Payback Period = 3 + [Initial Investment – (Cash Flow Year 1 + Cash Flow Year 2 + Cash Flow Year 3)] / Cash Flow Year 4

= 3 + [85,000 – 69,140] / 19,080

= 3 + 0.83 = 3.83 years

## QUESTION 5

Year | Cheap System | Expensive System | Present Value Factor at 10% | Present Value Cheap System | Present Value Expensive System |

0 | (%55,000) | ($95,000) | |||

1 | 28,000 | 40,000 | 0.909 | 25452 | 36360 |

2 | 20,000 | 20,000 | 0.826 | 16520 | 16520 |

3 | 10,000 | 20,000 | 0.751 | 7510 | 15020 |

4 | 5,500 | 10,000 | 0.683 | 3756.5 | 6830 |

5 | 4,500 | 10,000 | 0.621 | 2794.5 | 6210 |

6 | 10,000 | 0.564 | 5640 | ||

7 | 10,000 | 0.513 | 5130 | ||

8 | 10,000 | 0.467 | 4670 | ||

Total | 56033 | 96380 | |||

NPV | 1033 | 1380 |

**NPV _{Cheap} _{System} = **= 56033 – 55,000 = 1033

**NPV _{Expensive} _{System} = **= 96380 – 95,000 = 1380

**NPV****Cheap System ****= EAA****Cheap System ***** **EAACheap System = NPVCheap System / = 1033/ = 272.5

**NPV****Expensive System ****= EAA****Expensive System ***** ** EAAExpensive System = NPVExpensive System / = 1380/ = 258.67

*****NPV****Cheap System **is greater than **NPV****Expensive System**

- The Cheap System should be purchased.

## QUESTION 6

NPV if the system was operated for the full 4 years

Year | Initial Investment and Operating Cash Flow | Present Value Factor at 10% | Present Value |

0 | ($50,000) | ||

1 | 24,000 | 0.909 | 21,816 |

2 | 18,000 | 0.826 | 14,868 |

3 | 12,000 | 0.751 | 9,012 |

4 | 5,000 | 0.683 | 3,415 |

Total | 49,111 |

**NPV = **= 49,111 – 50,000 = -889

NPV_{1} if the system was abandoned at the end of Year 3

Year | Initial Investment and Cash Flow | Present Value Factor at 10% | Present Value |

0 | ($50,000) | ||

1 | 24,000 | 0.909 | 21,816 |

2 | 18,000 | 0.826 | 14,868 |

3 | 12,000 + 5,000 | 0.751 | 13,518 |

Total | 50,202 |

**NPV _{1} = **=50,202 – 50,000 = 202

NPV_{2} if system was abandoned at the end of Year 2 is:

Year | Initial Investment and Cash Flow | Present Value Factor at 10% | Present Value |

0 | ($50,000) | ||

1 | 24,000 | 0.909 | 21,816 |

2 | 18,000 + 20,000 | 0.826 | 31,388 |

Total | 53,204 |

**NPV _{2} = **= 53,204 – 50,000 = 3,204

NPV_{3} if system was abandoned at the end of Year 1 is:

Year | Initial Investment and Cash Flow | Present Value Factor at 10% | Present Value |

0 | ($50,000) | ||

1 | 24,000 + 30,000 | 0.909 | 49,086 |

Total | 49,086 |

**NPV _{1} = **= 49,086 – 50,000 = -914

Conclusion, NPV_{2} is the greatest, so David should abandon the system at the end the year 2. Economic life is 2 years.