You may buy now a Toyota Camry at a discount of $2500, or you can get financing

Question

You may buy now a Toyota Camry at a discount of $2500, or you can get financing at 0% APR for 72 months. If the car costs $24000 and your alternate car loan source has a 48 month loan at 3.6%, which offer do you accept? Assume your ordinary earnings is 2.4% per year, to be used as the discount rate in the Present Worth analysis. Your business receives a proposal to install a solar energy system on the roof. The system is estimated to be able to supply 450 kW-hr of power each month. Electricity currently costs you $0.10 per kW-hr. The system will be installed and the entire cost will be financed at 4% APY for 5 years. Assuming your business has an IRR of 10% per year, what total price would you be willing to pay to make this investment "breakeven" over a 10 year operating period? In other words, what initial system price has a PW equal to the PW of the monthly cost savings?

Explanation / Answer

Option 1: Suppose taking a discount of $ 2500, in that cash net payment of car is $24,000 - $2500 = $21,500 and assuming that for this amount taking a bank loan at 3.6% per annum for 48 months.

Monthly EMI = [P x R x (1+R)^N]/[(1+R)^N-1],

where P is loan amount or principal = $ 21,500

R is the interest rate per month = 3.6%/12 = 0.3%

and N is the number of monthly installments = 48

Monthly EMI = $ 481.61 per month

Option 2: Taking a car finance on amount $24,000 at 0% APR for 72 month

Monthly EMI = $ 312.75 per month

where P is loan amount or principal = $ 24,000

R is the interest rate per month = 0%

and N is the number of monthly installments = 72

Now present worth calculation at 2.4% per annum discounting rate or 0.2% per month discounting rate-

By using present worth analysis, Option 2 is better option.

Option 1 Option 2 month Net cash inflow/outflow (actual Dollars) Multiplied by Discounting Factor Equivalent Present Worth month Net cash inflow/outflow (actual Dollars) Multiplied by Discounting Factor Equivalent Present Worth 1 -481.61 (1+0.002)-1 -480.65 1 -312.75 (1+0.002)-1 -312.13 2 -481.61 (1+0.002)-2 -479.69 2 -312.75 (1+0.002)-2 -311.50 3 -481.61 (1+0.002)-3 -478.73 3 -312.75 (1+0.002)-3 -310.88 4 -481.61 (1+0.002)-4 -477.78 4 -312.75 (1+0.002)-4 -310.26 5 -481.61 (1+0.002)-5 -476.82 5 -312.75 (1+0.002)-5 -309.64 6 -481.61 (1+0.002)-6 -475.87 6 -312.75 (1+0.002)-6 -309.02 7 -481.61 (1+0.002)-7 -474.92 7 -312.75 (1+0.002)-7 -308.41 8 -481.61 (1+0.002)-8 -473.97 8 -312.75 (1+0.002)-8 -307.79 9 -481.61 (1+0.002)-9 -473.03 9 -312.75 (1+0.002)-9 -307.18 10 -481.61 (1+0.002)-10 -472.08 10 -312.75 (1+0.002)-10 -306.56 11 -481.61 (1+0.002)-11 -471.14 11 -312.75 (1+0.002)-11 -305.95 12 -481.61 (1+0.002)-12 -470.20 12 -312.75 (1+0.002)-12 -305.34 13 -481.61 (1+0.002)-13 -469.26 13 -312.75 (1+0.002)-13 -304.73 14 -481.61 (1+0.002)-14 -468.33 14 -312.75 (1+0.002)-14 -304.12 15 -481.61 (1+0.002)-15 -467.39 15 -312.75 (1+0.002)-15 -303.52 16 -481.61 (1+0.002)-16 -466.46 16 -312.75 (1+0.002)-16 -302.91 17 -481.61 (1+0.002)-17 -465.53 17 -312.75 (1+0.002)-17 -302.31 18 -481.61 (1+0.002)-18 -464.60 18 -312.75 (1+0.002)-18 -301.70 19 -481.61 (1+0.002)-19 -463.67 19 -312.75 (1+0.002)-19 -301.10 20 -481.61 (1+0.002)-20 -462.74 20 -312.75 (1+0.002)-20 -300.50 21 -481.61 (1+0.002)-21 -461.82 21 -312.75 (1+0.002)-21 -299.90 22 -481.61 (1+0.002)-22 -460.90 22 -312.75 (1+0.002)-22 -299.30 23 -481.61 (1+0.002)-23 -459.98 23 -312.75 (1+0.002)-23 -298.70 24 -481.61 (1+0.002)-24 -459.06 24 -312.75 (1+0.002)-24 -298.11 25 -481.61 (1+0.002)-25 -458.14 25 -312.75 (1+0.002)-25 -297.51 26 -481.61 (1+0.002)-26 -457.23 26 -312.75 (1+0.002)-26 -296.92 27 -481.61 (1+0.002)-27 -456.32 27 -312.75 (1+0.002)-27 -296.33 28 -481.61 (1+0.002)-28 -455.41 28 -312.75 (1+0.002)-28 -295.73 29 -481.61 (1+0.002)-29 -454.50 29 -312.75 (1+0.002)-29 -295.14 30 -481.61 (1+0.002)-30 -453.59 30 -312.75 (1+0.002)-30 -294.55 31 -481.61 (1+0.002)-31 -452.69 31 -312.75 (1+0.002)-31 -293.97 32 -481.61 (1+0.002)-32 -451.78 32 -312.75 (1+0.002)-32 -293.38 33 -481.61 (1+0.002)-33 -450.88 33 -312.75 (1+0.002)-33 -292.79 34 -481.61 (1+0.002)-34 -449.98 34 -312.75 (1+0.002)-34 -292.21 35 -481.61 (1+0.002)-35 -449.08 35 -312.75 (1+0.002)-35 -291.63 36 -481.61 (1+0.002)-36 -448.19 36 -312.75 (1+0.002)-36 -291.04 37 -481.61 (1+0.002)-37 -447.29 37 -312.75 (1+0.002)-37 -290.46 38 -481.61 (1+0.002)-38 -446.40 38 -312.75 (1+0.002)-38 -289.88 39 -481.61 (1+0.002)-39 -445.51 39 -312.75 (1+0.002)-39 -289.31 40 -481.61 (1+0.002)-40 -444.62 40 -312.75 (1+0.002)-40 -288.73 41 -481.61 (1+0.002)-41 -443.73 41 -312.75 (1+0.002)-41 -288.15 42 -481.61 (1+0.002)-42 -442.84 42 -312.75 (1+0.002)-42 -287.58 43 -481.61 (1+0.002)-43 -441.96 43 -312.75 (1+0.002)-43 -287.00 44 -481.61 (1+0.002)-44 -441.08 44 -312.75 (1+0.002)-44 -286.43 45 -481.61 (1+0.002)-45 -440.20 45 -312.75 (1+0.002)-45 -285.86 46 -481.61 (1+0.002)-46 -439.32 46 -312.75 (1+0.002)-46 -285.29 47 -481.61 (1+0.002)-47 -438.44 47 -312.75 (1+0.002)-47 -284.72 48 -481.61 (1+0.002)-48 -437.57 48 -312.75 (1+0.002)-48 -284.15 Total -22021.35 49 -312.75 (1+0.002)-49 -283.58 50 -312.75 (1+0.002)-50 -283.02 51 -312.75 (1+0.002)-51 -282.45 52 -312.75 (1+0.002)-52 -281.89 53 -312.75 (1+0.002)-53 -281.32 54 -312.75 (1+0.002)-54 -280.76 55 -312.75 (1+0.002)-55 -280.20 56 -312.75 (1+0.002)-56 -279.64 57 -312.75 (1+0.002)-57 -279.09 58 -312.75 (1+0.002)-58 -278.53 59 -312.75 (1+0.002)-59 -277.97 60 -312.75 (1+0.002)-60 -277.42 61 -312.75 (1+0.002)-61 -276.86 62 -312.75 (1+0.002)-62 -276.31 63 -312.75 (1+0.002)-63 -275.76 64 -312.75 (1+0.002)-64 -275.21 65 -312.75 (1+0.002)-65 -274.66 66 -312.75 (1+0.002)-66 -274.11 67 -312.75 (1+0.002)-67 -273.56 68 -312.75 (1+0.002)-68 -273.02 69 -312.75 (1+0.002)-69 -272.47 70 -312.75 (1+0.002)-70 -271.93 71 -312.75 (1+0.002)-71 -271.39 72 -312.75 (1+0.002)-72 -270.85 Total -20952.33

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.