Question

(Inspired by CT1 exam April '09) A company has agreed to rent a warehouse for 30 years. The rent will be paid quarterly in advance and will increase every three years at the rate of 3% per annum compound. The initial rent is set at £1,200,000 p.a. with the first payment due immediately. Calculate the NPV of the contract at a rate of interest of 5% p.a.

Answer 1

The NPV calculation for a 30-year, quarterly-paid, escalating lease requires discounting an annuity for each three-year period and summing the present values, considering the 3% escalation and 5% discount rate.

Step-by-step explanation:

The question involves calculating the net present value (NPV) of a warehouse rental contract, taking into account an increasing rent with quarterly payments in advance and an escalation rate. The initial annual rent is £1,200,000, and it increases every three years by 3% compound. The discount rate is 5% per annum. To calculate the NPV, you would need to discount all future payments back to their present value using the formula for annuities and the adjustment for the increasing rent. Quarterly payments require converting the annual payment into quarterly installments and discounting at a quarterly rate. The three-year escalation in rents necessitates calculating separate annuities for each three-year block and then discounting those back to the present using the discount rate.

For example, the first three years of payments would be an annuity with the initial rent divided by four (for quarterly payments), and each subsequent three-year block would involve calculating the increased payment due to the 3% compound escalation and then finding the present value of the new annuity.

One would continue this process for all ten three-year periods within the 30-year span, and sum all these present values to find the total NPV of the rental contract.

Answer 2

The Net Present Value (NPV) of the warehouse rental contract is calculated by discounting the future rent payments, which are made quarterly and increase by 3% every three years, using the given annual interest rate of 5% converted to a quarterly rate. The initial quarterly rent is £300,000, and the PV formula is applied to each series of payments with the adjusted rates and amounts.

Step-by-step explanation:

Calculation of Net Present Value (NPV)

To calculate the NPV of the warehouse rental contract, we need to discount the future rental payments to their present value using the given interest rate (5% per annum). Since rent will increase by 3% every three years compound, and payments are quarterly in advance, we must adjust the rent payments and discount rate accordingly.

Let's start by calculating the quarterly rent payment. The annual rent is £1,200,000. This gives us a quarterly payment of £1,200,000 / 4 = £300,000. However, we also need to calculate the increased payments starting every three years. To find the NPV, we apply the present value formula to each series of payments over the contract's lifecycle.

Present Value (PV) formula:

PV = PMT × ¹−(1 + i)⁻¹ / i

where PMT is the payment amount, and i is the discount rate per period.

For example, for the first three years (12 quarters), the payments remain at £300,000 each quarter. The first increase will occur at the start of the fourth year, and subsequent increases will occur every three years thereafter.

Each series of payments is discounted using the adjusted quarterly rate from the annual rate of 5%, which is (1 + 0.05)^(1/4) - 1. Then, we calculate the present value of each of the corresponding payment series using the adjusted rent amounts and compound the 3% rental increase every three years. Finally, summing the present values of all payment series gives the total NPV of the warehouse rent contract.