    # Capital Budgeting - Long Term Investment Analysis Illustration 92

If an investment project expenses \$5000, market rate of interest is \$10% per annum and it capitulate net return of \$7500 in the subsequent year. Must the investment in the project be made?

Solution

The net present value of the project is set by the following:

NPV    =          - Co + R1
1+i

Co       =          \$5000

i          =          10%

R1       =          \$7500

=          - 5000 + 7500
1 + 0.10

=          - 5000 + 7500 / 1.1

=          -5000 + 6818.2

=          \$1818.2

Therefore, carrying out this project will enhance wealth of the industry by \$1818.2. Hence, investment in this project must be made.

Illustration 93

Presume an industry is preparing to buy machinery which costs \$10000 carrying an interest of 50% per annum and prospected capitulate in the subsequent year would be 15000 and at the end of the subsequent year the machinery has no depreciated value. Is this worthy to sanction the project?

Solution

Net present value of the machinery:

NPV    =          - Co + R1
1+i

Co       =          \$10000

i          =          50%

R1       =          \$15000

NPV    =          - 10000 + 15000 / 1 + 0.50

=          - 10000 + 15000 / 1.50

=          - 10000 + 10000

NPV    =          \$0

1. Therefore, the net present value of the machinery is null. It is not worthy to make investment in this machinery.
1. Nevertheless it has to be noted that if the capitulate from the machinery in the subsequent year surpasses \$15000, its net present value will become positive and it will then be advantageous to buy it for the manufacturing of a commodity.
1. It has to be noted that if the capitulate in the subsequent year stays \$15000 but rate of interest drops below 50 %, the net present value will again become positive.

Illustration 94

Presume an industry is considering investing in a project. Its cost this year is \$50000 and its net capitulate next year would be \$75000 and its obsolete value would be null.

Determine the highest rate of interest at which the project must be undertaken.

Solution

To ascertain the necessary value of rate of interest (1) we have to make the net present value paritying to zero and thus,

NPV    =          - Co + R1        =          0
1+i

Co       =          \$50000

i           =          ?

R1       =          \$75000

- 50000 + 75000          =          0
1 + i

75000        =          50000
1 + i

75000        =          50000 (1 + i)

(1 + i)        =          75000  =          1.5
50000

i           =          1.5 – 1 =          0.5

1. This entails if the rate of interest is 0.50 that is 50%, the net present value of project is null.
1. Therefore, if the rate of interest drops below 50% the net present value will become positive.
1. Thus, the project should be undertaken for any value of the rate of interest below 50%.

Illustration 95

Presume an industry is bearing in mind to purchase machinery now for \$40000. The use of this machinery in the manufacturing process of a product creates industry’s net income to hike by \$20000 in every of the subsequent two year.

Presume the rate of interest as 5% and machinery posses no obsolete value. Is it desirable for the industry to buy the machinery?

Solution

NPV    =          - Co + R1        +          - Co + R2
1+i                              (1+i) ^2

Co       =          \$40000

i        =          5%

R1       =          \$20000

=          - 40000 + 20000          +          - 40000 + 20000
(1 + 0.05)                               (1 + 0.05) ^2

=          - 40000 + 20000          +          - 40000 + 20000
1.05                                        1.1025

=          - 40000 + 19048          +          - 40000 + 18140

=          20952     +          21860

=          \$42812

Therefore, the net present value of the machinery is positive and hence it will enhance the wealth of the industry by \$42812. It is thus advantageous to make investment in it.

Illustration 96

Two projects X and Y are suggested to an industry. Cost in the present year and net cash flow in the subsequent year of every industry is provided in a tablet. You are required to determine which project must be selected if market rate of interest is 20% per annum.

 Project Cost of current year Net cash flow in the subsequent year Project X \$200 millions \$250 millions Project Y \$300 millions \$360 millions

Solution

Net present value of Project X           =          - Co + R1
1+i

=          - 200 + 250
1+0.20

=          - 200 + 208                  =          8

Net present value of Project Y           =          - 300 + 360
1+0.20

=          - 300 + 300                  =          0

Therefore, net present value of Project X (8) is greater than the net present value of Y (0). Hence the industry should go on for Project X.

Illustration 97

Presume a bond capitulate a sum of \$9000 per annum imprecisely, beginning from a year now. Presume rate of interest as 9%. Calculate its present value.

Solution

Formula for computing the present value is

PV       =          R
i

R         =          \$9000

I           =          9%

=          9000    =          100000
0.09

This is for the reason that if \$100000 is invested at 9% of interest rate, it will capitulate \$9000 every year through life time.

That is
100000 x   9                =          9000
100

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