Question

Decision #1: Which set of Cash Flows is worth more now? Assume that your grandmother wants to give you generous gift. She wants you to choose which one of the following sets of cash flows you would like to receive: Option A: Receive a one-time gift of $ 10,000 today.

Option B: Receive a $1500 gift each year for the next 10 years. The first $1500 would be received 1 year from today.

Option C: Receive a one-time gift of $18,000 10 years from today. Compute the Present Value of each of these options if you expect the interest rate to be 3% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth ______today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect the interest rate to be 6% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Compute the Present Value of each of these options if you expect to be able to earn 9% annually for the next 10 years. Which of these options does financial theory suggest you should choose?

Option A would be worth $__________ today.

Option B would be worth $__________ today.

Option C would be worth $__________ today.

Financial theory supports choosing Option _______

Please show how this is done on Excel if possible, Thanks!

Answer 1

If discount rate is 3%
Option A	present worth of Option A	future value/(1+r)^n	10000/(1+3%)^0	10000
Option B	present worth of Option B	Annuity payment*PVAF at 3% for 10 Years	1500*8.5300	12795		0.74409391
PVAF at 3% for 10 Years	1-(1+r)^n -1 /r	1-(1.03)^-10/ 3%	.25590/3%	8.5300		0.25590609
option 3	Present value of cash flow	fv/(1+r)^n	18000/(1.03^10	13393.69		8.53020284
I will choose option 3 as it results in highest present value
if discount rate is 6%
Option A	present worth of Option A	future value/(1+r)^n	10000/(1+6%)^0	10000
Option B	present worth of Option B	Annuity payment*PVAF at 6% for 10 Years	1500*7.36	11040		0.55839478
PVAF at 6% for 10 Years	1-(1+r)^n -1 /r	1-(1.06)^-10/ 6%	.44160/6%	7.36		0.44160522
option 3	Present value of cash flow	fv/(1+r)^n	18000/(1.06)^10	10051.11		7.36008705
I will choose option 2 as it results in highest present value
if discount rate is 9%
Option A	present worth of Option A	future value/(1+r)^n	10000/(1+9%)^0	10000		0.42241081
Option B	present worth of Option B	Annuity payment*PVAF at 9% for 10 Years	1500*6.4166	9624.9		0.57758919
PVAF at 9% for 10 Years	1-(1+r)^n -1 /r	1-(1.09)^-10/ 9%	.5775/9%	6.41666667		6.4176577
option 3	Present value of cash flow	fv/(1+r)^n	18000/(1.09)^10	7603.39452
I will choose option 1 as it results in highest present value