Question

A robot from the year 3019 goes back in time to steal priceless objects. Unfortunately he must wait in a cave to return to the year 3019. He uses his loot to count how many years have passed. The robot has stolen 5 diamonds, 3 rubies, 8 emeralds, and 4 peals. Assume a Diamond, Ruby, Emerald, Pearl ordering with Diamonds being the most significant and Pearls being the least.

(a) How many years can the robot count?

(b) How many years do three of each jewel represent.

(c) What combination of jewels represents 500 years?

Answer 1

1. The AW value of defender is computed as follows,

AW Defender =-Initial investment x (A/P, r, N) – Annual expenses + MV at end of useful life x (A/P, r, N)

Initial investment = current MV + cost to upgrade

= $37,000 + $2,000 = $39,000

(A/P, 18%, 6) = 0.2859

Annual Expenses = $1,200

MV at end of useful life = -$1,600

(P/F, 18%, 6) = 0.3704

AW Defender = -39,000 (0.2859) – 1,200 – 1,600 (0.3704)

AW Defender = -$11,150 - $1,200 - $593 = $12,943

The AW value of Defender = -$12,943

1. The AW value of Challenger:

AW value of Challenger = -Initial investment x (A/P, r, N) – Annual expenses + MV at end of useful life x (A/P, r, N)

Initial investment = purchase price + installation cost

Initial investment = $53,000 + 5,300 = $58,300

Annual expenses = $900

Useful life = 10 years

Market value at end of useful life = $6,500

AW Challenger = -58,300 (A/P, 18%, 10) - $900 + $6,500 (P/F, 18%, 10)

AW Challenger = -58,300 (0.2225) – 900 + 6,500 (0.1911)

AW Challenger = -12,972 – 900 + 1,242

AW Challenger = -$12,630

Based the on the above computations the AW of Defender (-$12,943) is higher compared to the AW Challenger ($12,630). The Defender has highest cash outflows, hence the robot should be replaced right now.