Circle the best answer. Show calculations for each problem on a separate sheet o
ID: 1167010 • Letter: C
Question
Circle the best answer. Show calculations for each problem on a separate sheet of paper For the firm to break even ,500,000 and variable costs of S0.15 per unit produced. A company has annual fixed costs of $2 ifthey charge si production is nearest to what value? 85 for their product, the level of annual a) 375,000 b) 1,315,000 c) 1,351,000 d) 1,531,000 Which statement is not true with respect to estimating the economic impacts of proposed engineering projects? a) Order-of-magnitude estimates are used for high-level planning. b) Order-of-magnitude estimates are the most accurate type at about-3% to 5%. c) Increasing the accuracy of estimates requires added time and resources. d) Estimators tend to underestimate the magnitude of costs and to overestimate benefits. A 250-gallon reactor costs $780,000 when it was constructed 20 years ago. What would a 750-gallon model cost today if the power-sizing exponent is 0.56 and the construction cost index for such facilities has increased from 141 to 557 over the last 20 years? Choose the closest value. a) $0.45 million b) $1.69 million c) $1.47 million d) $5.65 million A deposit of $50,000 is made into an account that pays 10% compounded quarterly. The amount in the account after 10 years is nearest to which value? a) $81,445 b) $129,685 c) $132,665 d) $336,375 what value after 5 years? If you invest $40,000 in a stock whose value grows at 2% per year, your investment is nearest a) $40,800 b) $43,296 c) $44,164 d) $64,420Explanation / Answer
Solution:
1) Breakeven occurs when firm earns neither profit nor loss. So, at breakeven point, total cost, TC = total revenue, TR
Also, TC = fixed cost, FC + x*Variable cost, VC, x is the level of production
TC = 2,500,000 + 0.15*x
TR = p*x = 1.85*x
So, at breakeven, 2500000 + 0.15*x = 1.85*x
1.7*x = 2500000, giving us x = 1470588.24
So, level of production = 1,470,588, which is nearest to 1,531,000 among the given options. So, correct answer is d. 1,531,000
3) Since, in last 20 years, coonstruction cost index has increased from 141 to 557, ratio increase = 557/141 = 3.95 (approx)
So, present value/cost of 250 gallon reactor (which was purchased 10 years back) = cost of purchase*ratio-increase in that time period
= 780000*3.95 = 3,081,276.6
Now, cost of 250-gallon reactor/cost of 750-gallon reactor = (250/750)0.56 = 0.54 (approx)
so, on cross multiplying, cost of 750G R = cost of 250G R/0.54
Cost of 250G R = 3,081,276.6/0.54 = 5706067.78
Hence, today's cost of 750-gallon reactor = $5,706,068, which is closest to 5,650,000 among the given options. So, correct answer is d) $5.65 millions.
4) Principle amount deposited, P = $50,000, interest rate, i = 10%, no. of years, t = 10 years
Formula for quarterly compounded, accumulated amount, A = P (1 + i/4)4t
In this case, A = 50000*(1 + 0.1/4)4*10
A = 50000*(1.025)40 = 134,253.192.
So, accumulated amount after 10 years = $134,253. Clearly, among the provided options, it is nearest to $132,665. So, correct answer is c) $132,665.
5) It is again a form of compounding, just not quarterly but yearly.
So, following the same formula as above where now, P = 40,000, i = 2% = 0.02, t = 5 years
Using formula for yearly compounding: A = P*(1 + i)t
So, A = 40000*(1 + 0.02)5 = 40000*1.1041 = 44163.232
So, the investment value after 5 years = $44,163.232, which is clearly nearest to 44,164, among the given options. So, correct answer is c) $44,164