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Homework answers / question archive / Q1) What is the present value of a perpetuity consisting of equal annual payments of $38, where the first payment occurs one year from now, and the interest rate is 8% p
Q1) What is the present value of a perpetuity consisting of equal annual payments of $38, where the first payment occurs one year from now, and the interest rate is 8% p.a.?
Q2- What is the present value of a perpetuity consisting of equal payments of $76 every 6 months, where the first payment occurs 6 months from now, and the interest rate is 12% p.a.?
Q3- What is the present value of a perpetuity consisting of equal payments of $63 every 3 months, where the first payment occurs 3 months from now, and the interest rate is 12% p.a.?
q4- What is the present value of a growing perpetuity, where the first payment of $94 occurs one year from now, after which payments will grow at the constant rate of 3% p.a., and where the interest rate is 9% p.a.?
q5- What is the present value of a growing perpetuity, where the first payment of $28 occurs 6 months from now, after which payments will grow at the constant rate of 1.8% every 6 months, and where the interest rate is 10% p.a., compounded semi-annually?
1) Computation of Present Value of Perpetuity:
Present Value of Perpetuity = Cash Flow/Interest Rate
= $38/8%
Present Value of Perpetuity = $475
2) Computation of Present Value of Perpetuity:
Present Value of Perpetuity = Cash Flow/Interest Rate
= $76/6%
Present Value of Perpetuity = $1,266.67 or $1,263
Workings:
Interest Rate = 12%/2 = 6%
3) Computation of Present Value of Perpetuity:
Present Value of Perpetuity = Cash Flow/Interest Rate
= $63/3%
Present Value of Perpetuity = $2,100
Workings:
Interest Rate = 12%/4 = 3%
4) Computation of Present Value of Growing Annuity:
PV = D1/(Re-g)
= 94/(9%-3%)
PV = $1,566.67
So, Present Vlaue of Growing Annuity is $1,566.67
5) Computation of Present Value of Growing Annuity:
PV = D1/(Re-g)
Here,
Re = 10% per annum compounded semiannually
Calculation of interest for semiannual period
(1+x)2 = 1.10
1+x = 1.04881
x = 0.04881
Hence Semi annual compounding rate = 4.881%
Similarly we have to find out semi-annual growth rate
(1+y)2 = 1.018
1+y = 1.00896
y = 0.00896
Hence Semi annual growth rate is 0.896%
Substituting the above rates in the formula:
PV = 28/(0.04881-0.00896) = $702.65
Hence the present value of growing perpetuity is $702.65
