Question

A construction crane collapsed while working on a new building for Metro City. A pedestrian was killed. The husband of the victim is suing Metro City and the construction company. The city attorney, in consultation the city’s liability insurer and the construction company, has offered two out-of-court settlements to the husband of the victim. Here are the settlement options

Option 1: Four annual payments of $225,000 with the first payment one year from today.

Option 2: Five Payments of $200,000 with the payments one year, three years, five years, seven years, and nine years from today.

Assuming a 6% discount rate, which settlement option is the best from the perspective of Metro City?

Answer 1

The option better for Metro city would be the one which would result in lower cash outflow in present value terms.
Thus, for each of the option we need to calculate present value.
Calculation of present value of Option 1
Year	Cash flow	Discount factor @ 6%		Present value
1	225000	0.943396226	1/(1.06^1)	$212,264.15
2	225000	0.88999644	1/(1.06^2)	$200,249.20
3	225000	0.839619283	1/(1.06^3)	$188,914.34
4	225000	0.792093663	1/(1.06^4)	$178,221.07
				$779,648.76
Thus, present value of cash outflow is $779,648.76.
Calculation of present value of Option 2
Year	Cash flow	Discount factor @ 6%		Present value
1	200000	0.943396226	1/(1.06^1)	$188,679.25
3	200000	0.839619283	1/(1.06^3)	$167,923.86
5	200000	0.747258173	1/(1.06^5)	$149,451.63
7	200000	0.665057114	1/(1.06^7)	$133,011.42
9	200000	0.591898464	1/(1.06^9)	$118,379.69
				$757,445.85
Thus, present value of cash outflow is $757,445.85.
Metro city should select option 2 as present value of cash outflow is lower.