5. A five-star hotel decided to enter a long-term contract with an HVAC maintenance company. The HVAC maintenance company offers a starting price of P750,000 payable every end of the year for thirty...

Topic: Gradients

General Direction: Solve using Given-Required-Solution format. DO NOT USE EXCEL. Provide a Cash Flow Diagram (CFD).

Extracted text: 5. A five-star hotel decided to enter a long-term contract with an HVAC maintenance company. The HVAC maintenance company offers a starting price of P750,000 payable every end of the year for thirty years, with an annual increase of P25,000. The hotel wanted a uniform annual payment instead and asked the maintenance company to revise the contract prior to signing. What uniform annual payment does the maintenance company need to offer in the revised contract so that the present worth is the same as with the first offer? Assume 10% annual interest rate. 6. A company initially planned to slash their annual thanksgiving party spending from P75,000 to P40,000 held every year-end for ten years to increase their net profit. The CEO however changed his mind and decided to reduce the spending gradually over the course of ten years instead. If the approved yearly deductions follow a geometric gradient series, what is the yearly rate of deduction so that its present worth is the same as the present worth of the initial deduction plan. Annual interest rate is 5%.


Extracted text: Uniform Arithmetic Gradient Key words: increase or decrease by a uniform amount each period Ascending arithmetic progression P = PA + PG G[(1+ i)" – 1 PG i 1 i |(1+ i)"| [1-(1+i)¯ PA = A i Geometric Gradient Key words: increase / decrease by percentage Instead of fixed value P = A[1 - (1+ g/1+i)"] i-g where: P= Present of all cash flow between periods 1 and n A = Cash flow in period 1 g= rate of change per period i= effective interest rate per period