Question

Starwood Ltd is considering to invest in a new project. The project is expected to generate cash flows of $1,000 every four years forever with the first cash flow starting in year 2 and $4,000 every four years forever with the first cash flow starting in year 4. Suppose similar investments are paying a return of 10% p.a. compounded quarterly. How much should Starwood Ltd be prepared to pay for this project?

Answer 1

Effective Rate for 4 Years :
Rate per period	2.50%		10%/4
No. of periods	16
Effective Rate = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.025 ) ^ 16 ] - 1
= [ ( 1.025 ) ^ 16 ] - 1
= [ 1.4845 ] - 1
0.4845
EAR is 48.45 %
Here the time gap between CFs is 4 years. As thay are compounded quarterly, There will be 16 PERIODS for 4 Years.
PV of $ 1000 CF:
PV of CF at the end of Year 2 with out Year 2 CF = CF / Effective Rate
= $ 1000 / 48.45%
= $ 2063.98
Total PV of CF at Year 2 = $ 2063.98 + $ 1000
= $ 3063.98
Value Today = PV of Total CF at Year 2
Present Value:
PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods
Future Value	$              3,063.98
Int Rate	2.50%
Periods	8
Present Value = Future Value / ( 1 + r )^n
= $ 3063.98 / ( 1 + 0.025 ) ^ 8
= $ 3063.98 / ( 1.025 ) ^ 8
= $ 3063.98 / 1.2184
= $ 2514.75
PV of $ 4000 :
CF / Effective Rate
= $ 4000 / 48.45%
= $ 8255.93
To bring year 2 CFs into today's value, There is gap of 2 Years. Hence 2 * 4 qtrs.
Value of Project :
= $ 2514.75 + $ 8255.93
= $ 10770.68