Question

Your parents have come to you for financial advice because you have told them about this incredible finance course you are taking and they are paying for. Your parents have been offered an investment that will pay $100 per year forever and the first cash flow will occur 11 years from today. If interest rates are expected to be 6.125% forever;

a.         What is this investment worth today? HINT: be sure to include a timeline in your explanation to your parents. Show your work and explain your answer, not done in excel. b.  Your parents have been offered another investment that will pay $90 per year forever and the first cash flow will occur 11 years from today; however, the cash flow amounts are expected to grow at 1% forever. If interest rates are expected to be 6.125% forever, what is this investment worth today and which investment should they take? HINT: be sure to include a time line in your explanation to your parents. Show your work and formulas, timeline, not done in excel.

Answer 1

Part (a):

Cash flow is as follows:

                                                        $100             $100

                                                            ↑                    ↑

Year 0-------……..----------10-------------11---------------12------…….

Value of investment (perpetuity) one year before commencement (P_n)= C/r

Present worth =P_n/(1+r)^n

Where

C= yearly payment (given as $100)

r= interest rate (given as 6.125%) and

n= Period till commencement, less 1 = 10 years

Plugging the values,

Present worth= (100/0.06125)/(1+0.06125)^10

= 1632.65306/ 1.8335358 = $890.44

Part (b):

Cash flows will increase at 1% per year

Cash flow is as follows:

                                                        $90             $90.90         $91.81

                                                            ↑                    ↑                  ↑

Year 0-------……..----------10-------------11---------------12-------------13…….

Value of investment (growing perpetuity) one year before commencement (P_n)= C/(r-g)

Present worth =P_n/(1+r)^n

Where

C= First payment (given as $90)

r= interest rate (given as 6.125%)

g= Growth rate after first payment (given as 1%) and

n= Period till commencement, less 1 = 10 years

Plugging the values,

Present worth= (90/(0.06125-0.01))/(1+0.06125)^10

= 1714.28571/ 1.8335358 = $934.96