River Wild is considering purchasing a water park in , for . The new facility will generate annual net cash inflows of for years. Engineers estimate that the facility will remain useful for years and have no residual value. The company uses straight-line depreciation. Its owners want payback in less than five years and an ARR of % or more. Management uses a % hurdle rate on investments of this nature. Based on your reading, complete the given tasks:

a. Compute the payback period, the ARR, the NPV, and the approximate IRR of this investment.
b. Recommend whether the company should invest in this project?

The numbers are missing, so I looked for a similar question:

River Wild is considering purchasing a water park in Oakland, California, for $2,000,000. The new facility will generate annual net cash inflows of $510,000 for nine years. Engineers estimate that the facility will remain useful for nine years and have no residual value. The company uses straight-line depreciation. Its owners want payback in less than five years and an ARR of 12% or more. The management uses a 10% hurdle rate on investments of this nature.

a) Payback period = $2,000,000 / $510,000 = 3.92 years

ARR = net income / initial outlay

net income = net cash flow - depreciation expense = $510,000 - ($2,000,000/9) = $510,000 - $222,222 = $287,778

ARR = $287,778 / $2,000,000 = 0.1439 = 14.39%

NPV = -$2,000,000 + [$510,000 x 5.7590 (PV annuity factor, 10%, 9 periods)] = $937,090

using a financial calculator, the IRR = 20.87%

b) Since the NPV is positive, the payback period is less than 5 years, and the ARR is higher than expected, the project should be carried out.

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.