Consider a project that costs $380,000 today, provides an income of $120,000 per
ID: 1163716 • Letter: C
Question
Consider a project that costs $380,000 today, provides an income of $120,000 per year for four years, and costs $50,000 to dispose of in four years
Hello,
I would really appreciate help on this problem with a step by step solution. Please complete all parts of the problem. Thank you so much!
Consider a project that costs $380,000 today, provides an income of $120,000 per year for four years, and costs S50,000 to dispose of in four years. Assume that the first income payment comes in one year and the last payment in four years. Should the project be undertaken if the discount rate is 0%? How about ifthe discount rate is 2%? Is 5%? Is 10%? 9.Explanation / Answer
ANSWER:
1) At 0% discount rate
initial cost = $380,000
yearly income = $120,000
dispose cost at the end of 4th year = $50,000
We need to find the present worth at 0% discount rate.
pw = initial cost + yearly income(p/a,i,n) + disposal income at the end of 4th year(p/f,i,n)
pw = -380,000 + 120,000(p/a,0%,4) - 50,000(p/f,0%,4)
at 0% discount rate , the time value of money will not be there.
so pw = -380,000 + 120,000 * 4 - 50,000
pw = -380,000 + 480,000 - 50,000
pw = $50,000
2) At 2% discount rate
initial cost = $380,000
yearly income = $120,000
dispose cost at the end of 4th year = $50,000
We need to find the present worth at 2% discount rate.
pw = initial cost + yearly income(p/a,i,n) + disposal income at the end of 4th year(p/f,i,n)
pw = -380,000 + 120,000(p/a,2%,4) - 50,000(p/f,2%,4)
so pw = -380,000 + 120,000 * 3.808 - 50,000 * 0.9238
pw = -380,000 + 456,960 - 46,190
pw = $30,770
3) At 5% discount rate
initial cost = $380,000
yearly income = $120,000
dispose cost at the end of 4th year = $50,000
We need to find the present worth at 5% discount rate.
pw = initial cost + yearly income(p/a,i,n) + disposal income at the end of 4th year(p/f,i,n)
pw = -380,000 + 120,000(p/a,5%,4) - 50,000(p/f,5%,4)
so pw = -380,000 + 120,000 * 3.546 - 50,000 * 0.8227
pw = -380,000 + 425,520 - 41,135
pw = $4,385
4) At 10% discount rate
initial cost = $380,000
yearly income = $120,000
dispose cost at the end of 4th year = $50,000
We need to find the present worth at 10% discount rate.
pw = initial cost + yearly income(p/a,i,n) + disposal income at the end of 4th year(p/f,i,n)
pw = -380,000 + 120,000(p/a,10%,4) - 50,000(p/f,10%,4)
so pw = -380,000 + 120,000 * 3.17 - 50,000 * 0.683
pw = -380,000 + 380,400 - 34,150
pw = -$33,750
so the project could be undertaken when the discounts are 0% , 2% , 5% as the present worth is positive while at 10% discount rate the present worth is negative and hence the project should not be taken at 10% discount rate.