Question

Congratulations! You just won your lawsuit against a major corporation for unethical business practices. As part of the settlement, you have been given two options to receive your money.  The first option is receiving $2,000,000 at the beginning of each year for the next 5 years. The second option is that you can receive a lump sum payment today of $8.5 million. If the discount rate that you use to value the annuity is 6%, which option will provide you with the largest cash payout (ignoring taxes)?

		annuity stream
		lump sum payment
		the options are equivalent
		cannot be determined

Assume project A has cash flows over the next four years (in order) as follows: 1000, 1000, 1500, 1500. Project B has the following cash flows (in order) over the same four year period: 1500, 1500, 1000, 1000. If you plan to use the same discount rate for both projects, which of the following can never be true?

		Project A is more valuable than B.
		Project B is more valuable than A.
		Projects A and B have the same value.
		None of the above; each one of the above statements could be true in certain instances.

Answer 1

1) First we need to calculate present value of both options

Option 1) $2,000,000 at the beginning of each year for the next 5 years

Here formula of present value of annuity due can be used

Annuity = 2,000,000 $

r = rate of interest = 6%

n = n of years = 5

PV(annuity due) = Annuity[1-(1/(1+r)^n / r ] x (1+r)

= 2000000[1-(1/(1+6%)^5 / 6% ] x (1+6%)

= 2000000[1-(1/(1.06)^5 / 6%] x (1.06)

= 2000000[1-0.7473 / 6% ] x 1.06

= 2000000 x [0.2527/0.06] x 1.06

= 2000000 x 4.2124 x 1.06

= 8,930,211.25 $

Option 2) Receive a lump sum payment today of $8.5 million

Since payment is received today , PV of option 2 = $ 8,500,000

Ans) Annuity Stream

Reason: Since PV of annuity stream is greater than lump sum amount received today

2) Ans) Project A is more valuable than project B

Since total of cash inflow of both project are same, project with larger cash flow in earlier years will be more valuable. Further if 0% is used as dicount rate than both project will have same value. Only option that project A is more valuable than project B is not valid