Future Value Table: 24-Pet-B3 Petroleum Geology, May 2016, Q21

Question 21 — Future Value Table (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Initial purchase $25,000,000 at start of Year 1 (time zero); further $5,000,000 investments at the start of Years 3, 6 and 9; Hurdle Rate = 15%; 10-year holding period; inflation and taxes ignored. The exam's own column definitions use a “start of year = time zero” compounding convention: Expected Value at the start of year t = Expected Value at the start of year (t−1) + the return earned at the end of year (t−1) + any new investment made at the start of year t; the Return earned at the end of year t = (Expected Value at the start of year t) × Hurdle Rate.

Find. The Expected Value and Return columns for Years 1–10, and the minimum property value at Year 10 needed to meet the 15% hurdle rate.

Approach. Roll the recursive definition forward one year at a time: add each year's new investment to the running Expected Value, then earn a full year's return on that updated balance, carrying both forward into the next year.

Year 1 (initial purchase). $$EV_1 = 25{,}000\ \text{k\$}, \qquad Ret_1 = EV_1\times0.15 = 3{,}750\ \text{k\$}$$
Roll forward through Year 10, adding the $5,000k investments at the start of Years 3, 6 and 9 and compounding the running balance at 15%/yr each year (full table below).
Minimum value to meet the hurdle at Year 10 equals the Expected Value at the start of Year 10 plus the return earned by the end of Year 10: $$V_{min} = EV_{10} + Ret_{10} = 115{,}742.04 + 17{,}361.31 = \boxed{133{,}103.34\ \text{k\$}\ (\approx\ \$133.1\ \text{million})}$$ As a cross-check, this equals each cash investment compounded forward to the end of Year 10 at 15% and summed: $25{,}000(1.15)^{10}+5{,}000(1.15)^{8}+5{,}000(1.15)^{5}+5{,}000(1.15)^{2}=\boxed{133{,}103.34\ \text{k\$}}$.

Year	Investment (k$)	Cumulative Investment (k$)	Expected Value (k$)	Return @ 15% (k$)
1	25,000.00	25,000.00	25,000.00	3,750.00
2	0.00	25,000.00	28,750.00	4,312.50
3	5,000.00	30,000.00	38,062.50	5,709.38
4	0.00	30,000.00	43,771.88	6,565.78
5	0.00	30,000.00	50,337.66	7,550.65
6	5,000.00	35,000.00	62,888.30	9,433.25
7	0.00	35,000.00	72,321.55	10,848.23
8	0.00	35,000.00	83,169.78	12,475.47
9	5,000.00	40,000.00	100,645.25	15,096.79
10	0.00	40,000.00	115,742.04	17,361.31
Minimum value to meet Hurdle Rate (Yr 10)				133,103.34 k$

Topic: Future-value (forward-compounding) hurdle-rate screening

Key relations: EV_t = EV_t-1 + Ret_t-1 + Inv_t; Ret_t = EV_t×i; equivalently, each cash investment compounds forward as Inv_t(1+i)^11-t because the “start of year = time zero” convention gives an investment made at the start of year t a full (11−t) years of compounding through the end of Year 10.

Why this works: This is simply forward (future-value) compounding of a series of cash outlays made at different times, restated as a year-by-year running balance so each column can be graded independently; the closed-form sum of compounded investments must equal the recursive roll-forward exactly, which is a useful self-check.

Common pitfall: Using an exponent of (10−t) instead of (11−t) — because an investment at the start of year t earns a FULL year's return by the end of year t itself under this convention, it compounds for (11−t), not (10−t), years through the end of Year 10; this off-by-one is the single most common error in this table.

Source: Thompson & Wright, Oil Property Evaluation, Ch. on future value/hurdle-rate screening; COGEH Vol. 1.

Question 21 of 22: Future Value Table

Question 21 — Future Value Table (5 marks)