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Evaluation of proposals I

Evaluate different financial proposals including scholarships, investments, and purchases to determine their profitability based on interest rates and costs. Make informed decisions on financial feasibility.

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Evaluation of proposals I

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  1. Evaluation of proposalsI

  2. Problem 4-1 As a scholarship, you can receive $3,000 now. However, you must return $500 annually from the time of graduation (exactly four years from now) for 10 years. Assuming an annual interest rate of 10% per year, determine whether this proposal is profitable or not.

  3. 3000 4-1 4 13 0 500 PRevenue = 3000 P3 = 500×（P/A, 10%, 10)= 3072 PCost = 3072×(P/F, 10%, 3) = 2300 NPW = PRevenue－Pcost = 3000－ 2300 = 700 Ans: The proposal is profitable by NPW=700

  4. Problem 4-2 By introducing the computer system with an investment of $20,000, annual savings of $3,000 of the labor cost is expected. Assuming that the savings will last for 8 years, determine whether the introduction of the computer system is profitable or not. i=6% per year.

  5. 3000 0 4-2 8 20000 －1400 NPW = 3000×(P/A, 6%, 8) ＝ Ans:Since NPW＝－1400, the proposal is not profitable.

  6. Problem 4-3 The membership card of a tennis club costs $2,000. The price of this card is expected to become $4,000 in 10 years. Using a ROR method, determine whether the purchase of this card is profitable or not. i=10% per year.

  7. 4000 4-3(Use ROR method） 0 10 ROR (Rate of return): PRevenue = PCost 2000 2000 = 4000×(P/F, r%, 10) 0.5 = (P/F, r%, 10) r = 7%+ < 10% Ans: The proposal is not profitable.

  8. Problem 4-4 Which is more profitable: receipts of $5,000 forever, or receipts of $10,000 for ten years? i=10% per year.

  9. (A) (B) 4-4 10000 5000 ・・・・ ・・・・ 0 ∞ 0 10 NPWA = 5000×(P/A, 10%, ∞)= 50000 NPWB = 10000×(P/A, 10%, 10)= 61400 Which is more profitable? Ans: Latter（proposal B) is more profitable by NPW=11400.

  10. Problem 4-6 To increase the quality of the products, a new machine must be purchased. There are two candidates: machines A and B. The data of each machine are given as shown below. Assume that each machine has ten years of life. Which machine do you choose? i=16% per year. In order to judge that the choice of machine B is more profitable than the choice of machine A, how much increase in annual revenue of machine B will be needed?

  11. (B) (A) 14000 12000 4-6 0 0 10 10 7000 7000 10000 20000 NAWA = 5000－　10000 ×(A/P, 16%, 10) = 2931 NAWB = 7000－　20000 × (A/P, 16%, 10) = 2862 Ans: Machine A is more profitable by NAW=69 . For machine B to be a better choice, the annual revenue for B should increase by 69.

  12. Problem 4-7 SIME manufacturing is considering the replacement of the old machine. The new machine X will cost $16,000, its useful life is 8 years and disposal value in 8 years will be estimated to be $3,000. In addition, annual operating cost of $1,000 is needed. Meanwhile, the machine Y being used right now was purchased 4 years ago with the price of $20,000 and it can be used for 8 more years. The disposal value of the machine Y is estimated to be $2,000 in 8 years. The annual operating cost of this machine is $2,800. If the machine Y is replaced now, the machine Y can be sold with the price of $5,000. Assuming i=16% per year, determine whether the machine Y should be replaced with the machine X.

  13. Purchase of a new machine X (replacement) 4-7 Use machine Y 5000 3000 2000 1000 2800 The purchasing cost of machine Y is a sunk cost. 16000 PX=3000(P/F, 16%, 8)－1000(P/A, 16%, 8)－11000=-14425 PY=2000(P/F, 16%, 8)－2800(P/A, 16%, 8)=-11542 Px has a larger loss. Machine Y should be remained.

  14. Problem 4-8 A company is examining the following 8 proposals. The initial investment amount and annual return are listed in the table below. The life of each proposal is 10 years. Disposal value in 10 years is assumed to be zero for each proposal. Assume i=12% per year. At the right two columns of the table, value of the net annual worth and rate-of-return of each proposal are listed.

  15. Problem 4-8 (a) When 8 proposals are assumed to be mutually independent, select the best combination of proposals within the budget of $20,000 with i=12%. Assume that proposals are not divisible.

  16. (A) (F) (G) 4-8 (a) 2050 1800 650 ････ ････ ･･ ０ ０ ０ １０ １０ １０ 2000 5000 6000 Proposal A：　　2000 = 650×(P/A, r%, 10) r = 30% Proposal F：　NAW = 1800－50000 ×(A/P, 12%, 10) = 915 Proposal G：　NAW = 2050－60000 × (A/P, 12%, 10) = 988

  17. 4-8 (a) 34 33 30 28 26 24 22 20 F G 12% A D H C E B $20000 $3000 Ans : (a) F-G-A-D-C

  18. Problem 4-8 (b) When proposals are mutually exclusive, select the best proposal.

  19. 4-8 (b) (2) Since proposals are mutually exclusive, choose the proposal with the largest NAW. Ans: Proposal G

  20. Problem 4-10 Sun-Drop Doughnut factory is manufacturing 3,600 doughnuts everyday and distribute them to its sales stores. The selling price of a doughnut is 30 per unit. Material cost and other variable costs are 10 per unit, packaging cost is 5 for one dozen (12units) of doughnuts. Furthermore, 600,000 is necessary as a fixed cost such as maintenance cost of the store and monthly salary for employees. Answer the following questions, assuming 20 working days per month.

  21. Problem 4-10 (a) The factory was in full operation. The maximum daily production volume of the doughnuts was limited to 3,600 units. One day, at the time of delivery to sales stores, 50 dozens of doughnuts (both 600 doughnuts and 50 packaging boxes) were damaged and discarded. How much was the loss due to this damage?

  22. 4-10 (a) Ans: 18000

  23. Problem 4-10 (b) To solve the problem of the damage in question (a), the company considered the purchase of a plastic container box. In a container, 50 dozen of doughnuts could be packed. The life of the plastic container was estimated to be 60 months. If the plastic container could solve the damaging problem, how much was the maximum allowable investment cost for the plastic container? Assume that the accident happens once a month in average. i=1% per month

  24. 4-10 (b) 18000 ･････････ 0 60 X (P/A, 1%, 60) =1/(A/P, 1%, 60) = 1/0.02224=44.96 X = 18000×(P/A, 1%,60) = 809,280

  25. Problem 4-10 (c) By the introduction of the plastic container, the damaging problem was solved. After a few moths, because of an appearance of a strong doughnuts company competitor, Sun-Drop’s daily production volume dropped to 3,000 units. One day, while delivering doughnuts to the sales stores, three dozens of doughnuts were dropped and reproduced (new boxes were needed). How much loss might be attributed to this accident?

  26. 4-10 (c) Ans: 375

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