1) (Present value of a growing? perpetuity)  What is the present value of a perpetual stream of cash flows that pays ?$4,500 at the end of year one and the annual cash flows grow at a rate of 4?% per year? indefinitely, if the appropriate discount rate is 15?%? What if the appropriate discount rate is 13?%?   2)   A company is expected to pay a dividend of $3

1) 

Computation of Present Value of a Growing Perpetuity:

Present Value of a Growing Perpetuity = Cash flow for year 1/(Discount rate-Growth rate)

When Discount Rate is 15%:

Present Value of a Growing Perpetuity = $4,500/(0.15-0.04) = $4,500/0.11 = $40,909.09 or $40,909

When Discount Rate is 13%:

Present Value of a Growing Perpetuity = $4,500/(0.13-0.04) = $4,500/0.09 = $50,000

2) 

Computation of Dividend Growth Rate:

Current Stock Price = Dividend for Next Year / (Required Rate of Return - Growth Rate)

$42 = $3.25/(10% - Growth Rate)

$42*(10% - Growth Rate) = $3.25

$4.2 - $42* Growth Rate = $3.25

$4.2 - $3.25 = $42* Growth Rate

$0.95 = $42* Growth Rate

Growth Rate = $0.95/$42 = 2.26%

3) 

If you borrow 700,000 to buy a home, what do you suppose your monthly payment will be? Suppose a 30-year mortgage and a fixed 7% interest rate.

Computation of Monthly Payment using PMT Function in Excel:

=pmt(rate,nper,-pv,fv)

Here,

PMT = Monthly Payment = ?

Rate = 7%/12 = 0.5833% compounded monthly

Nper = 30 years * 12 months = 360 months

PV = $700,000

FV = 0

Substituting the values in formula:

=pmt(0.5833%,360,-700000,0)

PMT or Monthly Payment = $4,656.93

If you invest $1500 each year for 35 years, how much will you have at the end of 35 years assuming a 10% annual rate?

Computation of Future Value using FV Function in Excel:

=-fv(rate,nper,pmt,-pv)

Here,

FV = Future Value = ?

Rate = 10%

Nper = 35 Years

PMT = $1,500

PV = 0

Substituting the values in formula:

=-fv(10%,35,1500,0)

FV or Future Value = $406,536.55