Question

Simes Innovations, Inc., is negotiating to purchase exclusive rights to manu- facture and market a solar-powered toy car. The car’s inventor has offered Simes the choice of either a one-time payment of $1,500,000 today or a series of five year-end payments of $385,000. a) If Simes has a cost of capital of 9%, which form of payment should it choose? 
 b) What yearly payment would make the two offers identical in value at a cost of capital of 9%? 
 c) Would your answer to part a of this problem be different if the yearly payments were made at the beginning of each year? Show what difference, if any, that 
change in timing would make to the present value calculation. 
 d) Theafter-taxcashinflowsassociatedwiththispurchaseareprojectedtoamount to $250,000 per year for 15 years. Will this factor change the firm’s decision about how to fund the initial investment? 


Answer 1

Answer a
Calculation of present value of yearly payments of $385000 using 9% cost of capital as discount rate
We can use the present value of annuity formula to calculate this value.
Present Value of annuity = P x [1 - (1+r)^-n]/r
P = annual payment = $385000
r = cost of capital = 9%
n = number of annual payments = 5
Present Value of annuity = 385000 x [1 - (1+0.09)^-5]/0.09
Present Value of annuity = 385000 x 3.889651
Present Value of annuity = 1497516
Present value of yearly payments of $385000 for 5 years = $14,97,516
The above value is less than that of lumsum payment of $15,00,000 which is to be received today,
hence Simes Innovations, Inc. should choose option of a one-time payment of $1,500,000 today.
Answer b
We need to find out the yearly payment which makes the present value equivalent to $15,00,000
We can use the present value of annuity formula to calculate this yearly payment.
Present Value of annuity = P x [1 - (1+r)^-n]/r
Present Value of annuity = $15,00,000
P = annual payment = ?
r = cost of capital = 9%
n = number of annual payments = 5
1500000 = P x [1 - (1+0.09)^-5]/0.09
1500000 = P x 3.889651
P = 385639
Yearly payment of $3,85,639 would make the two offers identical in value at a cost of capital of 9%.
Answer c
Calculation of present value of yearly payments of $385000 if the yearly payments were made at the beginning of each year
We can use the present value of annuity due formula to calculate this value.
Present Value of annuity = P + {P x [1 - (1+r)^-(n-1)]/r}
P = annual payment = $385000
r = cost of capital = 9%
n = number of annual payments = 5
Present Value of annuity = 385000 + {385000 x [1 - (1+0.09)^-(5-1)]/0.09}
Present Value of annuity = 385000 + {385000 x 3.239720}
Present Value of annuity = 385000 + 1247292
Present Value of annuity = 1632292
Present value of yearly payments of $385000 for 5 years = $16,32,292
The above value is more than that of lumsum payment of $15,00,000 which is to be received today,
hence Simes Innovations, Inc. should choose option of a yearly payment of $3,85,000.
Yes , the answer in Part a would be different if the yearly payments were made at the beginning of each year.