Question

An investor purchased, for an initial cost of £9.5 million, an office block to be rented out to other businesses. The investor spent a further £2 million on renovating the building three months after purchase An agreement has been made with the tenant who will start using the office block exactly half a year after the purchase date. The tenant will pay rent to the investor for ten years and will then immediately purchase the building from the company for £15.5 million. The first year's rent has been set at £760,000 per annum payable half-yearly in advance. The agreement states that, at the start of every second year (from the start of the rental period), the annual rent will increase by a rate of 5.5% per annum on a compound basis Assuming that rental income is received as expected and the company makes a rate of return of 8% per annum on the investment, calculate the investor's present value of the proceeds, in millions, from this project at the time of purchase. (Total 14 marks]

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Answer 1

	Present Value (PV) of Cash Flow:
	(Cash flow)/((1+i)^N)
	i=discount rate=Rate of return =8%=0.08
	N=Year of Cash flow
		N	CF			PV=CF/(1.08^N)
		Year	Cash Flow	CALCULATIONS		Present Value
	Initial Cash Flow at year 0	0	-£   9,500,000			-£       9,500,000
	Cash flow at year 0.25(after 3 months)	0.25	-£   2,000,000			-£       1,961,887
	First half yearly rent in advance	0.5	£        380,000	(760000/2)		£            365,655
	2nd installment of first year rent	1	£        380,000			£            351,852
	First installment of second year rent	1.5	£        380,000			£            338,570
	2nd installment of second year rent	2	£        380,000			£            325,789
	First installment of third year rent	2.5	£        400,900	(760000*1.055)/2		£            330,732
	2nd installment of third year rent	3	£        400,900			£            318,247
	First installment of fourth year rent	3.5	£        400,900			£            306,234
	2nd installment of fourth year rent	4	£        400,900			£            294,673
	First installment of fifth year rent	4.5	£        422,950	(400900*1.055)		£            299,145
	2nd installment of fifth year rent	5	£        422,950			£            287,852
	First installment of sixth year rent	5.5	£        422,950			£            276,986
	2nd installment of sixth year rent	6	£        422,950			£            266,530
	First installment of Seventh year rent	6.5	£        446,212	(422950*1.055)		£            270,574
	2nd installment of Seventh year rent	7	£        446,212			£            260,360
	First installment of eighth year rent	7.5	£        446,212			£            250,532
	2nd installment of eighth year rent	8	£        446,212			£            241,074
	First installment of ninth year rent	8.5	£        470,753	(446212*1.055)		£            244,732
	2nd installment of ninth year rent	9	£        470,753			£            235,494
	First installment of tenth year rent	9.5	£        470,753			£            226,604
	2nd installment of tenth year rent	10	£        470,753			£            218,050
	Cash Flow from Sale of the building	10	£ 15,500,000			£        7,179,499
					SUM	£        1,427,298
	Net Present value of proceeds	£          1,427,298
	Net Present value of proceeds	£                     1.43	million