Question

A firm is considering a project that will yield $10,000 per year for 10 years. The required return on this project is 12.05%, compounded monthly. What is the maximum amount that the firm should be willing to invest in the project to accept this project

Answer 1

Answer:

$695,603.10

Explanation:

The maximum amount that the firm would be willing to invest in the project to accept it can be calculated using the present value (PV) of an ordinary annuity stated as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PV = Present value or the maximum amount to invest?

P = yearly yield = $10,000

r = required return rate = 12.05% annually = (12.05% ÷ 12) monthly = 1.0041667% monthly or 0.010041667

n = number of period = 10 years = 10 × 12 months = 120 months

Substituting the values into equation (1), we have:

PV = 10,000 × [{1 - [1 ÷ (1+0.010041667)]^120} ÷ 0.010041667]

     = 10,000 × [{1 - [1 ÷ 1.010041667]^120} ÷ 0.010041667]

     = 10,000 × [{1 - [0.990058165590509]^120} ÷ 0.010041667]

      = 10,000 × [{1 - 0.301498531063694} ÷ 0.010041667]

      = 10,000 × [0.698501468936306 ÷ 0.010041667]

      = 10,000 × 69.5603099501613

PV = $695,603.10

The maximum amount that the firm would be willing to invest in the project to accept it is $695,603.10 .

Answer 2

Answer:

The maximum amount that the firm should invest in the project $695,603.10

Explanation:

The applicable formula in this scenario is the present value of an ordinary annuity,modified for timing of the cash flows,which is given below:

PV=A*(1-(1+r)^-N)/r

PV is the unknown

A is the periodic inflow of $10,000

r is the rate of return of 12.05% divided by 12 months i.e 12.05%/12=0.010041667

N is the number of years multiplied by 12 months i,e 10*12=120

PV=10000

annuity factor=(1-(1+r)^-N)/r

annuity factor=1-(1+0.010041667 )^-120/0.010041667

annuity factor=(1-0.301498531 )/0.010041667

annuity factor=69.56030996

PV=69.56030996 *10000

PV=$695,603.10