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Homework answers / question archive / 1) What is the maximum that should be invested in a project at time zero if the inflows are estimated at $4,000 annually for 4 years, and the cost of capital is 10 percent? Write your answer with two decimal point
1) What is the maximum that should be invested in a project at time zero if the inflows are estimated at $4,000 annually for 4 years, and the cost of capital is 10 percent? Write your answer with two decimal point.
2) What is the present value of a risk-free bond with a face value of $2000, a maturity of four years, annual coupon payments, a coupon rate of 5% if the interest rate is 10%?
3) What is the present value of a perpetuity that pays out $100 annually forever if the interest rate is 10%?
1) We can calculate the present value by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Present value
Rate = 10%
Nper = 4 periods
Pmt = $4,000
FV = $0
Substituting the values in formula:
= -pv(10%,4,4000,0)
= $12,679.46
2) Computation of the present value:-
Present value = (Coupon payment*((1-1/(1+rate)^n)/rate)) + (FV/(1+rate)^n)
Here,
Coupon payment = $2,000*5% = $100
PV = ($100*((1-1/(1+10%)^4)/10%)) + ($2,000/(1+10%)^4)
= ($100*3.16987) + ($2,000/1.46410)
= $316.99 + $1,366.03
= $1,683.01
3) Computation of the present value of perpetuity:-
PV of perpetuity = Perpetuity / Interest rate
= $100 / 10%
= $1,000
