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

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