Discounting, inflation and capital costs (and converting costs into IUS$) Lecture 5 Damian Walker

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2 Discounting, inflation and capital costs (and converting costs into IUS$) Lecture 5 Damian Walker

3 Aim of the lecture To provide conceptual and practical insight into how to adjust costs for differential timing

4 Structure of lecture Discounting: costs and benefits Annualising capital costs Adjusting for inflation Purchasing power parity: converting costs into IUS$

5 Time preference Would you prefer to have $100 now or in the future? Positive rate of time preference Why? live now, pay later attitude future is uncertain might expect to be wealthier in the future

6 Discounting costs Future streams of costs are discounted to reflect time preference and presented in terms of their present value We do this by using a discount factor Discount factor = 1 / (1+r) n where n = years in the future, r = discount rate Costs of year n multiplied by discount factor

7 Discount factors for present value: discount rate (r) = 5% Year (1+r) n ( ) 1 = ( ) 2 = ( ) 3 = ( ) 4 = ( ) 5 = Discount factor 1 / (1+r) n

8 Example If cost was the only deciding factor, which project would you invest in? Assume a 5% discount rate Also assume costs are incurred at the beginning of each time period Y1 Y2 Y3 Y4 Y5 Total Project A $100 $100 $100 $100 $100 $500 Project B $ $500 Project C $500 $500

9 Example Discount factor (5%) Project A Project B Project C Y1 Y2 Y3 Y4 Y5 Total

10 Which discount rate? Interest rate on a risk-free investment Rate used by a particular country or agency Rate used in literature: range 3-10% 3 Rate recommended by guidelines Carry out sensitivity analysis

11 Discounting health outcomes General consensus that future costs should be discounted However, economists do not agree that health outcomes should be discounted And those who agree, disagree about the rate But if discount at lower rate than costs projects become more desirable if we delay their implementation (Keeler & Cretin 1983) So soft recommendation is to discount at same rate as costs and carry out sensitivity analysis

12 Keeler & Cretin paradox Costs Effects CE ratio Programme Now Year 1 Year 2 Now Year 1 Year 2 Implemented today Delayed 1 year

14 Do discount rates differ in LDCs? (Poulos & Whittington 2000) Individuals time preferences for saving lives were measured in Bulgaria, Ethiopia, Indonesia, Mozambique Uganda and Ukraine using a statedpreference method Households in LDCs attach much less value to lives saved in the future than to lives saved today Relationship between time preference and income, life expectancy and education not consistent across countries. Other factors are important, e.g. perceived mortality risk, political instability and culture

15 Topical example: the Stern report treasury.gov.uk/independent_reviews/stern_review_economics_climate_c te_c hange/stern_review_report.cfm The Stern report was commissioned by the British government to review the economics of climate change It became controversial among economists because of Sir Nicholas decision to choose a social discount rate of 0.1% Sir Nicholas argued that, because climate change economics requires a time horizon of centuries, the use of a typical discount rate would assign almost no current value to benefits accruing in, say, the 23 rd century But how can we say that our great-great great-great grandchildren are worth less than we are worth ourselves?

16 Intergenerational equity Therefore, he argues for a discount rate of 0.1% Such a near-zero rate places a much higher present-day value on benefits accruing centuries into the future, and thus makes a stronger case for spending money now What do you think?

17 Individual s s time preference Well-known men discount the future more steeply than women But assumed way person discounts a stable personality trait and arbitrary Wilson & Daly (2003) assumed men discount more steeply due to male reproductive imperative score often, score early and, above all, score when you can!

18 Carpe diem? Developed an experiment men who had seen pictures of attractive women discounted the future more steeply than they had before an I I want-that that-now pathway had been activated in their brains (women who had seen pictures of hot cars discounted the future more steeply than they had before. But the statistical significance of this finding disappeared after routine adjustments)

19 Opportunity costs Recall from Monday s s lecture that we need to estimate shadow prices / social value of resources: where goods have a yield over a period of time: capital goods

20 Annualisation Capital items purchased in previous years have a cost today Annualisation permits capital costs to be converted to their annual equivalent, or implicit rental value, and thus added to annual recurrent costs It involves spreading the cost of the capital item over its life, but also takes into account the possible earnings that the money could have made if it had not been tied up in the purchase of the capital item

21 Annualisation of capital items Annual financial cost = cost / expected length of life Annual economic cost = cost / annualising factor AF = (1 - DF) / r where DF = 1 / (1 + r) n, n = expected length of life and r = discount rate

22 Annualisation factors Source: UNAIDS. Costing Guidelines for HIV Prevention Strategies, 2000.

23 Question Single $5,000 piece of capital equipment (no re- sale value) useful life of 7 years discount rate of 5% What is the annual financial cost? What is the annual economic cost?

24 Answer

25 Adjusting for inflation Inflation: process by which general prices increase and money loses value When comparing data from different years adjust to constant / real terms Inflate / deflate prices by inflation adjustment factor (IAF) IAF = indicator of inflation in base year / indicator of inflation in past year Examples: CPI ( GDP deflator ( both and more ( TISTICS/0,,contentMDK: ~pagePK: ~piPK: ~theSitePK:239419,00.html)

26 Example Cost per bed-day day in 2003 costs = $45 How much is this in 2006 costs? CPI in 2003 = CPI in 2006 = 181.2

27 Answer

28 Concept of purchasing power parity Captures the notion that a dollar should buy the same amount in all countries Exchange rate should move towards the rate that equalises the prices of an identical basket of goods and services in each country The Economist uses a McDonald s s Big Mac, and more recently a Starbucks tall-latte, latte, is their basket the Big Mac PPP is the exchange rate that would mean Big Macs cost the same in America as abroad comparing official exchange rates with PPPs indicates whether a currency is under- or over-valued valued

29 Question A Big Mac cost $3.10 in the US on 22 nd May 2006 In China, it cost 10.5 Yuan Using the actual exchange rate the Big Mac cost only $1.31 ($1 = 8.02 Yuan) What is the implied PPP of the dollar? Is the Yuan over- or under-valued?

30 The Hamburger Standard Country BigMac Price Local Currency US dollars Actual Exchange Rate 1 USD = Over(+) / Under(-) Valuation against dollar, % Purchasing Power Price United States $ Argentina Peso Australia A$ Brazil Real Britain Canada C$ China Yuan Euro area Hong Kong HK$ Hungary Forint Indonesia Rupiah14, ,710 Japan Malaysia M$ Mexico Peso Poland Zloty Russia Rouble Singapore s$ South Africa Rand South Korea Won2, Sweden Skr Switzerland SFr Thailand Baht

31 From purchasing power of currencies to purchasing power of local wages Kenya Pakistan India Colombia Ukraine Peru Romania Mexico Venezuela Indonesia Lithuania Phillipines Slovakia Nigeria Chile Thailand Estonia Argentina Poland Hungary Brazil Czech Rep Slovenia Turkey Portugal South Africa United States Minutes of work required to buy a Big Mac (2003)

32 Converting costs into IUS$ WHO has developed PPPs An international dollar has the same purchasing power as the US$ has in the United States To convert local currency units to international dollars, divide the local currency unit by the PPP conversion factor

33 Example using Bangladesh data 2000 PPP = international dollar is equal to Taka for the year official exchange rate ( US$1 = Question convert 10,000 Taka into US$ and IUS$ (all in 2000 prices)

34 Answer

35 Summary Discounting costs should be discounted benefits less clear no consensus regarding appropriate discount rate, so use sensitivity analysis to assess robustness of findings to changes in the rate Capital costs should be annualised to spread value of item over its lifetime and to capture opportunity cost of tying-up funds in the purchase of the item

36 Summary Inflation CPI or GDP deflators can be used to adjust prices for inflation Purchasing power parity IUS$ is a hypothetical currency that has the same purchasing power that the US$ has in the US at a given point in time it is used to make comparisons both between countries and over time

37 Further reading Keeler, EB and Cretin S. Discounting of life saving and other non monetary effects. Management Science 1983; 29: Poulos C, Whittington D. Time preferences for life- saving programs: evidence from six less developed countries. Environmental Science and Technology 2000; 34: Wilson M, Daly M. Do pretty women inspire men to discount the future? Proc Biol Sci ; 271 Suppl 4: S

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