Question

Financial Management

Question 1

John met his insurance agent to discuss the purchase of an insurance plan to fund his 8 year-old daughter's university education in 11 years' time. The payout from the insurance company is as follows:

* Receive $30,000 at the begining of each year for 4 years with the first receipt starting 11 years from today.

The insurance company had 3 payment proposals:

Proposal 1:

* Pay $35,000 today

Proposal 2:

* Beginning 2 years from today, pay $8,000 each year for the next 8 years.

Proposal 3:

* Beginning 2 years from today, make payments each year for the next 8 years. The first payment is $7,000 and the amount increases by 5% each year.

(a) Calculate the present value of each proposal. Use a 10% discount rate. (7m)

(b) Which proposal should John choose? Explain. (5m)

(c) If the discount rate is not given to you, what would be an appropriate discount rate to use? (3m)

Answer 1

Evaluating the PV of the Proposals:

Proposal 1:

PV=35000

Proposal 2:

Beginning 2 years from today, pay $8,000 each year for the next 8 years.

PV at end Yr. 2 of the( PV of ordinary annuity of $ 8000 for i=10% & n=8 )

ie. PV at yr. 2 end of (8000*(1-1.1^-8)/0.1)

ie.PV at Yr. 2 end of of 42679.81

ie.42679.81/1.1^2=

35272.57

Proposal 3:

Beginning 2 years from today, make payments each year for the next 8 years. The first payment is $7,000 and the amount increases by 5% each year.

PV at end Yr. 2 of the( PV of growing annuity of $ 7000 for i=10% & n=8 & g= 5%)

ie. PV at yr. 2 end of (7000/(10%-5%))*(1-(1.05/1.1)^8)

ie.PV at Yr. 2 end of of 43505.86

ie.43505.86/1.1^2=

35955.26

(b)John should choose proposal 1 as it is the LEAST investment at time t= 0

(c) If the discount rate is not given to you, the appropriate discount rate to use

will be the IRR which equates the investment options & the insurance co.'s payout options,

ie.Matching the PV of the outflow with that of the inflows.

PV of payout from the insurance company at 10%

We substitute r , where ever there is 10% in this calculation used

PV at Yr.0 of the (PV of Annuity due of $ 30000 at Year 10 end /Yr.11 beg. at 10%p.a.)

ie. PV of (30000*(1-1.1^-4)/0.1)*(1.1)

ie. PV of 104605.56

104605.56/1.1^10=

40329.97

Pl.NOTE:The above has been done just to make it easy for substituting with r (not needed in this solution)

For Proposal 1:

PV of Outflow=PV of Inflow

ie.35000=((30000*(1-(1+r)^-4)/r)*(1+r))/(1+r)^10

Solving in an online equation solver, we get the IRR or r as

11.38%

For Proposal 2 :

PV of Outflow=PV of Inflow

((8000*(1-(1+r)^-8)/r))/(1+r)^2=((30000*(1-(1+r)^-4)/r)*(1+r))/(1+r)^10

Solving in an online equation solver, we get the IRR or r as

12.75%

For Proposal 3:

PV of Outflow=PV of Inflow

((7000/(r-5%))*(1-(1.05/(1+r))^8))/(1+r)^2=((30000*(1-(1+r)^-4)/r)*(1+r))/(1+r)^10

Solving in an online equation solver, we get the IRR or r as

18.29%